text: Euclid ("Eukleids" ; fl. 300 BCE), sometimes called Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "father of geometry". He was active in Alexandria during the reign of Ptolemy I (323283 BCE). His "Elements" is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the "Elements", Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor.

text: Euclid

text: Eukleids

text: fl

text: BCE

text: sometimes

text: called

text: Euclid

text: of

text: Alexandria

text: to

text: distinguish

text: him

text: from

text: Euclides

text: of

text: Megara

text: was

text: Greek

text: mathematician

text: often

text: referred

text: to

text: as

text: the

text: father

text: of

text: geometry

text: He

text: was

text: active

text: in

text: Alexandria

text: during

text: the

text: reign

text: of

text: Ptolemy

text: BCE

text: His

text: Elements

text: is

text: one

text: of

text: the

text: most

text: influential

text: works

text: in

text: the

text: history

text: of

text: mathematics

text: serving

text: as

text: the

text: main

text: textbook

text: for

text: teaching

text: mathematics

text: especially

text: geometry

text: from

text: the

text: time

text: of

text: its

text: publication

text: until

text: the

text: late

text: or

text: early

text: century

text: In

text: the

text: Elements

text: Euclid

text: deduced

text: the

text: principles

text: of

text: what

text: is

text: now

text: called

text: Euclidean

text: geometry

text: from

text: small

text: set

text: of

text: axioms

text: Euclid

text: also

text: wrote

text: works

text: on

text: perspective

text: conic

text: sections

text: spherical

text: geometry

text: number

text: theory

text: and

text: rigor

text: Geometry (from the ; "geo-" "earth", "-metron" "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer.

text: Geometry

text: from

text: the

text: geo-

text: earth

text: -metron

text: measurement

text: is

text: branch

text: of

text: mathematics

text: concerned

text: with

text: questions

text: of

text: shape

text: size

text: relative

text: position

text: of

text: figures

text: and

text: the

text: properties

text: of

text: space

text: mathematician

text: who

text: works

text: in

text: the

text: field

text: of

text: geometry

text: is

text: called

text: geometer

text: In mathematics, solid geometry is the traditional name for the geometry of three-dimensional Euclidean space.

text: In

text: mathematics

text: solid

text: geometry

text: is

text: the

text: traditional

text: name

text: for

text: the

text: geometry

text: of

text: three

text: dimensional

text: Euclidean

text: space

text: The term proposition has a broad use in contemporary philosophy. It is used to refer to some or all of the following: the primary bearers of truth-value, the objects of belief and other "propositional attitudes" (i.e., what is believed, doubted, etc.), the referents of that-clauses, and the meanings of declarative sentences. Propositions are the sharable objects of attitudes and the primary bearers of truth and falsity. This stipulation rules out certain candidates for propositions, including thought- and utterance-tokens which are not sharable, and concrete events or facts, which cannot be false.

text: The

text: term

text: proposition

text: has

text: broad

text: use

text: in

text: contemporary

text: philosophy

text: It

text: is

text: used

text: to

text: refer

text: to

text: some

text: or

text: all

text: of

text: the

text: following

text: the

text: primary

text: bearers

text: of

text: truth

text: value

text: the

text: objects

text: of

text: belief

text: and

text: other

text: propositional

text: attitudes

text: i.e.

text: what

text: is

text: believed

text: doubted

text: etc

text: the

text: referents

text: of

text: that

text: clauses

text: and

text: the

text: meanings

text: of

text: declarative

text: sentences

text: Propositions

text: are

text: the

text: sharable

text: objects

text: of

text: attitudes

text: and

text: the

text: primary

text: bearers

text: of

text: truth

text: and

text: falsity

text: This

text: stipulation

text: rules

text: out

text: certain

text: candidates

text: for

text: propositions

text: including

text: thought-

text: and

text: utterance

text: tokens

text: which

text: are

text: not

text: sharable

text: and

text: concrete

text: events

text: or

text: facts

text: which

text: can

text: not

text: be

text: false

text: A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, and plasma), and is the only state with a definite volume but no fixed shape. A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Water is, by far, the most common liquid on Earth. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly constant density. A distinctive property of the liquid state is surface tension, leading to wetting phenomena.

text: liquid

text: is

text: nearly

text: incompressible

text: fluid

text: that

text: conforms

text: to

text: the

text: shape

text: of

text: its

text: container

text: but

text: retains

text: nearly

text: constant

text: volume

text: independent

text: of

text: pressure

text: As

text: such

text: it

text: is

text: one

text: of

text: the

text: four

text: fundamental

text: states

text: of

text: matter

text: the

text: others

text: being

text: solid

text: gas

text: and

text: plasma

text: and

text: is

text: the

text: only

text: state

text: with

text: definite

text: volume

text: but

text: no

text: fixed

text: shape

text: liquid

text: is

text: made

text: up

text: of

text: tiny

text: vibrating

text: particles

text: of

text: matter

text: such

text: as

text: atoms

text: held

text: together

text: by

text: intermolecular

text: bonds

text: Water

text: is

text: by

text: far

text: the

text: most

text: common

text: liquid

text: on

text: Earth

text: Like

text: gas

text: liquid

text: is

text: able

text: to

text: flow

text: and

text: take

text: the

text: shape

text: of

text: container

text: Most

text: liquids

text: resist

text: compression

text: although

text: others

text: can

text: be

text: compressed

text: Unlike

text: gas

text: liquid

text: does

text: not

text: disperse

text: to

text: fill

text: every

text: space

text: of

text: container

text: and

text: maintains

text: fairly

text: constant

text: density

text: distinctive

text: property

text: of

text: the

text: liquid

text: state

text: is

text: surface

text: tension

text: leading

text: to

text: wetting

text: phenomena

text: Paint is any liquid, liquefiable, or mastic composition that, after application to a substrate in a thin layer, converts to a solid film. It is most commonly used to protect, color, or provide texture to objects. Paint can be made or purchased in many colorsand in many different types, such as watercolor, synthetic, etc. Paint is typically stored, sold, and applied as a liquid, but most types dry into a solid.

text: Paint

text: is

text: any

text: liquid

text: liquefiable

text: or

text: mastic

text: composition

text: that

text: after

text: application

text: to

text: substrate

text: in

text: thin

text: layer

text: converts

text: to

text: solid

text: film

text: It

text: is

text: most

text: commonly

text: used

text: to

text: protect

text: color

text: or

text: provide

text: texture

text: to

text: objects

text: Paint

text: can

text: be

text: made

text: or

text: purchased

text: in

text: many

text: colorsand

text: in

text: many

text: different

text: types

text: such

text: as

text: watercolor

text: synthetic

text: etc

text: Paint

text: is

text: typically

text: stored

text: sold

text: and

text: applied

text: as

text: liquid

text: but

text: most

text: types

text: dry

text: into

text: solid

text:
Mathematical analysis is the branch of mathematics dealing with limits
and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

text: Mathematical

text: analysis

text: is

text: the

text: branch

text: of

text: mathematics

text: dealing

text: with

text: limits

text: and

text: related

text: theories

text: such

text: as

text: differentiation

text: integration

text: measure

text: infinite

text: series

text: and

text: analytic

text: functions

text: In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory consists of an axiomatic system and all its derived theorems. An axiomatic system that is completely described is a special kind of formal system. A formal theory typically means an axiomatic system, for example formulated within model theory. A formal proof is a complete rendition of a mathematical proof within a formal system.

text: In

text: mathematics

text: an

text: axiomatic

text: system

text: is

text: any

text: set

text: of

text: axioms

text: from

text: which

text: some

text: or

text: all

text: axioms

text: can

text: be

text: used

text: in

text: conjunction

text: to

text: logically

text: derive

text: theorems

text: theory

text: consists

text: of

text: an

text: axiomatic

text: system

text: and

text: all

text: its

text: derived

text: theorems

text: An

text: axiomatic

text: system

text: that

text: is

text: completely

text: described

text: is

text: special

text: kind

text: of

text: formal

text: system

text: formal

text: theory

text: typically

text: means

text: an

text: axiomatic

text: system

text: for

text: example

text: formulated

text: within

text: model

text: theory

text: formal

text: proof

text: is

text: complete

text: rendition

text: of

text: mathematical

text: proof

text: within

text: formal

text: system

text: In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of "n"-dimensional Euclidean space. For "n" = 1, 2, or 3, it coincides with the standard measure of length, area, or volume. In general, it is also called n"-dimensional volume, n"-volume, or simply volume. It is used throughout real analysis, in particular to define Lebesgue integration. Sets that can be assigned a Lebesgue measure are called Lebesgue measurable; the measure of the Lebesgue measurable set "A" is denoted by ("A").

text: In

text: measure

text: theory

text: the

text: Lebesgue

text: measure

text: named

text: after

text: French

text: mathematician

text: Henri

text: Lebesgue

text: is

text: the

text: standard

text: way

text: of

text: assigning

text: measure

text: to

text: subsets

text: of

text: dimensional

text: Euclidean

text: space

text: For

text: or

text: it

text: coincides

text: with

text: the

text: standard

text: measure

text: of

text: length

text: area

text: or

text: volume

text: In

text: general

text: it

text: is

text: also

text: called

text: dimensional

text: volume

text: volume

text: or

text: simply

text: volume

text: It

text: is

text: used

text: throughout

text: real

text: analysis

text: in

text: particular

text: to

text: define

text: Lebesgue

text: integration

text: Sets

text: that

text: can

text: be

text: assigned

text: Lebesgue

text: measure

text: are

text: called

text: Lebesgue

text: measurable

text: the

text: measure

text: of

text: the

text: Lebesgue

text: measurable

text: set

text: is

text: denoted

text: by

text: In geometric measurements, length is the most extended dimension of an object. In the International System of Quantities, length is any quantity with dimension distance. In other contexts "length" is the measured dimension of an object. For example, it is possible to cut a length of a wire which is shorter than wire thickness.

text: In

text: geometric

text: measurements

text: length

text: is

text: the

text: most

text: extended

text: dimension

text: of

text: an

text: object

text: In

text: the

text: International

text: System

text: of

text: Quantities

text: length

text: is

text: any

text: quantity

text: with

text: dimension

text: distance

text: In

text: other

text: contexts

text: length

text: is

text: the

text: measured

text: dimension

text: of

text: an

text: object

text: For

text: example

text: it

text: is

text: possible

text: to

text: cut

text: length

text: of

text: wire

text: which

text: is

text: shorter

text: than

text: wire

text: thickness

text: A wire is a single, usually cylindrical, flexible strand or rod of metal. Wires are used to bear mechanical loads or electricity and telecommunications signals. Wire is commonly formed by drawing the metal through a hole in a die or draw plate. Wire gauges come in various standard sizes, as expressed in terms of a gauge number. The term "wire" is also used more loosely to refer to a bundle of such strands, as in "multistranded wire", which is more correctly termed a wire rope in mechanics, or a cable in electricity.

text: wire

text: is

text: single

text: usually

text: cylindrical

text: flexible

text: strand

text: or

text: rod

text: of

text: metal

text: Wires

text: are

text: used

text: to

text: bear

text: mechanical

text: loads

text: or

text: electricity

text: and

text: telecommunications

text: signals

text: Wire

text: is

text: commonly

text: formed

text: by

text: drawing

text: the

text: metal

text: through

text: hole

text: in

text: die

text: or

text: draw

text: plate

text: Wire

text: gauges

text: come

text: in

text: various

text: standard

text: sizes

text: as

text: expressed

text: in

text: terms

text: of

text: gauge

text: number

text: The

text: term

text: wire

text: is

text: also

text: used

text: more

text: loosely

text: to

text: refer

text: to

text: bundle

text: of

text: such

text: strands

text: as

text: in

text: multistranded

text: wire

text: which

text: is

text: more

text: correctly

text: termed

text: wire

text: rope

text: in

text: mechanics

text: or

text: cable

text: in

text: electricity

text:
Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.
Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container, i. e. the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces.

text: Volume

text: is

text: the

text: quantity

text: of

text: three

text: dimensional

text: space

text: enclosed

text: by

text: closed

text: surface

text: for

text: example

text: the

text: space

text: that

text: substance

text: solid

text: liquid

text: gas

text: or

text: plasma

text: or

text: shape

text: occupies

text: or

text: contains

text: Volume

text: is

text: often

text: quantified

text: numerically

text: using

text: the

text: SI

text: derived

text: unit

text: the

text: cubic

text: metre

text: The

text: volume

text: of

text: container

text: is

text: generally

text: understood

text: to

text: be

text: the

text: capacity

text: of

text: the

text: container

text: the

text: amount

text: of

text: fluid

text: gas

text: or

text: liquid

text: that

text: the

text: container

text: could

text: hold

text: rather

text: than

text: the

text: amount

text: of

text: space

text: the

text: container

text: itself

text: displaces

text: Real analysis (traditionally, the theory of functions of a real variable) is a branch of mathematical analysis dealing with the real numbers and real-valued functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real numbers, and continuity, smoothness and related properties of real-valued functions.

text: Real

text: analysis

text: traditionally

text: the

text: theory

text: of

text: functions

text: of

text: real

text: variable

text: is

text: branch

text: of

text: mathematical

text: analysis

text: dealing

text: with

text: the

text: real

text: numbers

text: and

text: real

text: valued

text: functions

text: of

text: real

text: variable

text: In

text: particular

text: it

text: deals

text: with

text: the

text: analytic

text: properties

text: of

text: real

text: functions

text: and

text: sequences

text: including

text: convergence

text: and

text: limits

text: of

text: sequences

text: of

text: real

text: numbers

text: the

text: calculus

text: of

text: the

text: real

text: numbers

text: and

text: continuity

text: smoothness

text: and

text: related

text: properties

text: of

text: real

text: valued

text: functions

text: Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects.

text: Set

text: theory

text: is

text: branch

text: of

text: mathematical

text: logic

text: that

text: studies

text: sets

text: which

text: informally

text: are

text: collections

text: of

text: objects

text: Although

text: any

text: type

text: of

text: object

text: can

text: be

text: collected

text: into

text: set

text: set

text: theory

text: is

text: applied

text: most

text: often

text: to

text: objects

text: that

text: are

text: relevant

text: to

text: mathematics

text: The

text: language

text: of

text: set

text: theory

text: can

text: be

text: used

text: in

text: the

text: definitions

text: of

text: nearly

text: all

text: mathematical

text: objects

text: The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces), for which the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration.

text: The

text: surface

text: area

text: of

text: solid

text: object

text: is

text: measure

text: of

text: the

text: total

text: area

text: that

text: the

text: surface

text: of

text: the

text: object

text: occupies

text: The

text: mathematical

text: definition

text: of

text: surface

text: area

text: in

text: the

text: presence

text: of

text: curved

text: surfaces

text: is

text: considerably

text: more

text: involved

text: than

text: the

text: definition

text: of

text: arc

text: length

text: of

text: one

text: dimensional

text: curves

text: or

text: of

text: the

text: surface

text: area

text: for

text: polyhedra

text: i.e.

text: objects

text: with

text: flat

text: polygonal

text: faces

text: for

text: which

text: the

text: surface

text: area

text: is

text: the

text: sum

text: of

text: the

text: areas

text: of

text: its

text: faces

text: Smooth

text: surfaces

text: such

text: as

text: sphere

text: are

text: assigned

text: surface

text: area

text: using

text: their

text: representation

text: as

text: parametric

text: surfaces

text: This

text: definition

text: of

text: surface

text: area

text: is

text: based

text: on

text: methods

text: of

text: infinitesimal

text: calculus

text: and

text: involves

text: partial

text: derivatives

text: and

text: double

text: integration

text: Quantity is a property that can exist as a magnitude or multitude. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value in terms of a unit of measurement. Quantity is among the basic classes of things along with quality, substance, change, and relation. Some quantities are such by their inner nature (as number), while others are functioning as states (properties, dimensions, attributes) of things such as heavy and light, long and short, broad and narrow, small and great, or much and little. A small quantity is sometimes referred to as a quantulum.

text: Quantity

text: is

text: property

text: that

text: can

text: exist

text: as

text: magnitude

text: or

text: multitude

text: Quantities

text: can

text: be

text: compared

text: in

text: terms

text: of

text: more

text: less

text: or

text: equal

text: or

text: by

text: assigning

text: numerical

text: value

text: in

text: terms

text: of

text: unit

text: of

text: measurement

text: Quantity

text: is

text: among

text: the

text: basic

text: classes

text: of

text: things

text: along

text: with

text: quality

text: substance

text: change

text: and

text: relation

text: Some

text: quantities

text: are

text: such

text: by

text: their

text: inner

text: nature

text: as

text: number

text: while

text: others

text: are

text: functioning

text: as

text: states

text: properties

text: dimensions

text: attributes

text: of

text: things

text: such

text: as

text: heavy

text: and

text: light

text: long

text: and

text: short

text: broad

text: and

text: narrow

text: small

text: and

text: great

text: or

text: much

text: and

text: little

text: small

text: quantity

text: is

text: sometimes

text: referred

text: to

text: as

text: quantulum

text: Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or compound molecules made from a variety of atoms (e.g. carbon dioxide). A gas mixture would contain a variety of pure gases much like the air. What distinguishes a gas from liquids and solids is the vast separation of the individual gas particles. This separation usually makes a colorless gas invisible to the human observer. The interaction of gas particles in the presence of electric and gravitational fields are considered negligible as indicated by the constant velocity vectors in the image. One type of commonly known gas is steam.

text: Gas

text: is

text: one

text: of

text: the

text: four

text: fundamental

text: states

text: of

text: matter

text: the

text: others

text: being

text: solid

text: liquid

text: and

text: plasma

text: pure

text: gas

text: may

text: be

text: made

text: up

text: of

text: individual

text: atoms

text: e.g.

text: noble

text: gas

text: like

text: neon

text: elemental

text: molecules

text: made

text: from

text: one

text: type

text: of

text: atom

text: e.g.

text: oxygen

text: or

text: compound

text: molecules

text: made

text: from

text: variety

text: of

text: atoms

text: e.g.

text: carbon

text: dioxide

text: gas

text: mixture

text: would

text: contain

text: variety

text: of

text: pure

text: gases

text: much

text: like

text: the

text: air

text: What

text: distinguishes

text: gas

text: from

text: liquids

text: and

text: solids

text: is

text: the

text: vast

text: separation

text: of

text: the

text: individual

text: gas

text: particles

text: This

text: separation

text: usually

text: makes

text: colorless

text: gas

text: invisible

text: to

text: the

text: human

text: observer

text: The

text: interaction

text: of

text: gas

text: particles

text: in

text: the

text: presence

text: of

text: electric

text: and

text: gravitational

text: fields

text: are

text: considered

text: negligible

text: as

text: indicated

text: by

text: the

text: constant

text: velocity

text: vectors

text: in

text: the

text: image

text: One

text: type

text: of

text: commonly

text: known

text: gas

text: is

text: steam

text: Algebra (from Arabic ""al-jabr"" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.

text: Algebra

text: from

text: Arabic

text: al

text: jabr

text: meaning

text: reunion

text: of

text: broken

text: parts

text: is

text: one

text: of

text: the

text: broad

text: parts

text: of

text: mathematics

text: together

text: with

text: number

text: theory

text: geometry

text: and

text: analysis

text: In

text: its

text: most

text: general

text: form

text: algebra

text: is

text: the

text: study

text: of

text: mathematical

text: symbols

text: and

text: the

text: rules

text: for

text: manipulating

text: these

text: symbols

text: it

text: is

text: unifying

text: thread

text: of

text: almost

text: all

text: of

text: mathematics

text: As

text: such

text: it

text: includes

text: everything

text: from

text: elementary

text: equation

text: solving

text: to

text: the

text: study

text: of

text: abstractions

text: such

text: as

text: groups

text: rings

text: and

text: fields

text: The

text: more

text: basic

text: parts

text: of

text: algebra

text: are

text: called

text: elementary

text: algebra

text: the

text: more

text: abstract

text: parts

text: are

text: called

text: abstract

text: algebra

text: or

text: modern

text: algebra

text: Elementary

text: algebra

text: is

text: generally

text: considered

text: to

text: be

text: essential

text: for

text: any

text: study

text: of

text: mathematics

text: science

text: or

text: engineering

text: as

text: well

text: as

text: such

text: applications

text: as

text: medicine

text: and

text: economics

text: Abstract

text: algebra

text: is

text: major

text: area

text: in

text: advanced

text: mathematics

text: studied

text: primarily

text: by

text: professional

text: mathematicians

text: An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek "axíma" 'that which is thought worthy or fit' or 'that which commends itself as evident.'

text: An

text: axiom

text: or

text: postulate

text: is

text: statement

text: that

text: is

text: taken

text: to

text: be

text: true

text: to

text: serve

text: as

text: premise

text: or

text: starting

text: point

text: for

text: further

text: reasoning

text: and

text: arguments

text: The

text: word

text: comes

text: from

text: the

text: Greek

text: axíma

text: that

text: which

text: is

text: thought

text: worthy

text: or

text: fit

text: or

text: that

text: which

text: commends

text: itself

text: as

text: evident

text: Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.

text: Space

text: is

text: the

text: boundless

text: three

text: dimensional

text: extent

text: in

text: which

text: objects

text: and

text: events

text: have

text: relative

text: position

text: and

text: direction

text: Physical

text: space

text: is

text: often

text: conceived

text: in

text: three

text: linear

text: dimensions

text: although

text: modern

text: physicists

text: usually

text: consider

text: it

text: with

text: time

text: to

text: be

text: part

text: of

text: boundless

text: four

text: dimensional

text: continuum

text: known

text: as

text: spacetime

text: The

text: concept

text: of

text: space

text: is

text: considered

text: to

text: be

text: of

text: fundamental

text: importance

text: to

text: an

text: understanding

text: of

text: the

text: physical

text: universe

text: However

text: disagreement

text: continues

text: between

text: philosophers

text: over

text: whether

text: it

text: is

text: itself

text: an

text: entity

text: relationship

text: between

text: entities

text: or

text: part

text: of

text: conceptual

text: framework

text: In mathematics, a real number is a value that represents a quantity along a line. The adjective "real" in this context was introduced in the 17th century by René Descartes, who distinguished between real and imaginary roots of polynomials.

text: In

text: mathematics

text: real

text: number

text: is

text: value

text: that

text: represents

text: quantity

text: along

text: line

text: The

text: adjective

text: real

text: in

text: this

text: context

text: was

text: introduced

text: in

text: the

text: century

text: by

text: René

text: Descartes

text: who

text: distinguished

text: between

text: real

text: and

text: imaginary

text: roots

text: of

text: polynomials

text: Number theory or, in older usage, arithmetic is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline. Number theorists study prime numbers as well as the properties of objects made out of integers (e.g., rational numbers) or defined as generalizations of the integers (e.g., algebraic integers).

text: Number

text: theory

text: or

text: in

text: older

text: usage

text: arithmetic

text: is

text: branch

text: of

text: pure

text: mathematics

text: devoted

text: primarily

text: to

text: the

text: study

text: of

text: the

text: integers

text: It

text: is

text: sometimes

text: called

text: The

text: Queen

text: of

text: Mathematics

text: because

text: of

text: its

text: foundational

text: place

text: in

text: the

text: discipline

text: Number

text: theorists

text: study

text: prime

text: numbers

text: as

text: well

text: as

text: the

text: properties

text: of

text: objects

text: made

text: out

text: of

text: integers

text: e.g.

text: rational

text: numbers

text: or

text: defined

text: as

text: generalizations

text: of

text: the

text: integers

text: e.g.

text: algebraic

text: integers

text: Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a gas does. The atoms in a solid are tightly bound to each other, either in a regular geometric lattice (crystalline solids, which include metals and ordinary ice) or irregularly (an amorphous solid such as common window glass).

text: Solid

text: is

text: one

text: of

text: the

text: four

text: fundamental

text: states

text: of

text: matter

text: the

text: others

text: being

text: liquid

text: gas

text: and

text: plasma

text: It

text: is

text: characterized

text: by

text: structural

text: rigidity

text: and

text: resistance

text: to

text: changes

text: of

text: shape

text: or

text: volume

text: Unlike

text: liquid

text: solid

text: object

text: does

text: not

text: flow

text: to

text: take

text: on

text: the

text: shape

text: of

text: its

text: container

text: nor

text: does

text: it

text: expand

text: to

text: fill

text: the

text: entire

text: volume

text: available

text: to

text: it

text: like

text: gas

text: does

text: The

text: atoms

text: in

text: solid

text: are

text: tightly

text: bound

text: to

text: each

text: other

text: either

text: in

text: regular

text: geometric

text: lattice

text: crystalline

text: solids

text: which

text: include

text: metals

text: and

text: ordinary

text: ice

text: or

text: irregularly

text: an

text: amorphous

text: solid

text: such

text: as

text: common

text: window

text: glass

text: The International System of Units (SI) specifies a set of seven base units from which all other SI units of measurement are derived. Each of these other units (SI derived units) is either dimensionless or can be expressed as a product of (positive or negative, but usually integral) powers of one or more of the base units.

text: The

text: International

text: System

text: of

text: Units

text: SI

text: specifies

text: set

text: of

text: seven

text: base

text: units

text: from

text: which

text: all

text: other

text: SI

text: units

text: of

text: measurement

text: are

text: derived

text: Each

text: of

text: these

text: other

text: units

text: SI

text: derived

text: units

text: is

text: either

text: dimensionless

text: or

text: can

text: be

text: expressed

text: as

text: product

text: of

text: positive

text: or

text: negative

text: but

text: usually

text: integral

text: powers

text: of

text: one

text: or

text: more

text: of

text: the

text: base

text: units

text: In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces. It is named after the Ancient Greek mathematician Euclid of Alexandria. The term "Euclidean" distinguishes these spaces from other types of spaces considered in modern geometry. Euclidean spaces also generalize to higher dimensions.

text: In

text: geometry

text: Euclidean

text: space

text: encompasses

text: the

text: two

text: dimensional

text: Euclidean

text: plane

text: the

text: three

text: dimensional

text: space

text: of

text: Euclidean

text: geometry

text: and

text: certain

text: other

text: spaces

text: It

text: is

text: named

text: after

text: the

text: Ancient

text: Greek

text: mathematician

text: Euclid

text: of

text: Alexandria

text: The

text: term

text: Euclidean

text: distinguishes

text: these

text: spaces

text: from

text: other

text: types

text: of

text: spaces

text: considered

text: in

text: modern

text: geometry

text: Euclidean

text: spaces

text: also

text: generalize

text: to

text: higher

text: dimensions

text: In mathematics, especially in set theory, a set "A" is a subset of a set "B", or equivalently "B" is a superset of "A", if "A" is "contained" inside "B", that is, all elements of "A" are also elements of "B". "A" and "B" may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment.

text: In

text: mathematics

text: especially

text: in

text: set

text: theory

text: set

text: is

text: subset

text: of

text: set

text: or

text: equivalently

text: is

text: superset

text: of

text: if

text: is

text: contained

text: inside

text: that

text: is

text: all

text: elements

text: of

text: are

text: also

text: elements

text: of

text: and

text: may

text: coincide

text: The

text: relationship

text: of

text: one

text: set

text: being

text: subset

text: of

text: another

text: is

text: called

text: inclusion

text: or

text: sometimes

text: containment

text: The International System of Quantities (ISQ) is a system based on seven base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. Other quantities such as area, pressure, and electrical resistance are derived from these base quantities by clear, non-contradictory equations. The ISQ defines the quantities that are measured with the SI units and also includes many other quantities in modern science and technology. The ISQ is defined in the international standard ISO/IEC 80000, and was finalised in 2009 with the publication of ISO 80000-1.

text: The

text: International

text: System

text: of

text: Quantities

text: ISQ

text: is

text: system

text: based

text: on

text: seven

text: base

text: quantities

text: length

text: mass

text: time

text: electric

text: current

text: thermodynamic

text: temperature

text: amount

text: of

text: substance

text: and

text: luminous

text: intensity

text: Other

text: quantities

text: such

text: as

text: area

text: pressure

text: and

text: electrical

text: resistance

text: are

text: derived

text: from

text: these

text: base

text: quantities

text: by

text: clear

text: non

text: contradictory

text: equations

text: The

text: ISQ

text: defines

text: the

text: quantities

text: that

text: are

text: measured

text: with

text: the

text: SI

text: units

text: and

text: also

text: includes

text: many

text: other

text: quantities

text: in

text: modern

text: science

text: and

text: technology

text: The

text: ISQ

text: is

text: defined

text: in

text: the

text: international

text: standard

text: ISO

text: IEC

text: and

text: was

text: finalised

text: in

text: with

text: the

text: publication

text: of

text: ISO

text: René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 159611 February 1650) was a French philosopher, mathematician, and scientist. Dubbed the father of modern western philosophy, much of subsequent Western philosophy is a response to his writings, which are studied closely to this day. He spent about 20 years of his life in the Dutch Republic.

text: René

text: Descartes

text: Latinized

text: Renatus

text: Cartesius

text: adjectival

text: form

text: Cartesian

text: March

text: February

text: was

text: French

text: philosopher

text: mathematician

text: and

text: scientist

text: Dubbed

text: the

text: father

text: of

text: modern

text: western

text: philosophy

text: much

text: of

text: subsequent

text: Western

text: philosophy

text: is

text: response

text: to

text: his

text: writings

text: which

text: are

text: studied

text: closely

text: to

text: this

text: day

text: He

text: spent

text: about

text: years

text: of

text: his

text: life

text: in

text: the

text: Dutch

text: Republic

text: In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces.

text: In

text: physics

text: and

text: mathematics

text: the

text: dimension

text: of

text: mathematical

text: space

text: or

text: object

text: is

text: informally

text: defined

text: as

text: the

text: minimum

text: number

text: of

text: coordinates

text: needed

text: to

text: specify

text: any

text: point

text: within

text: it

text: Thus

text: line

text: has

text: dimension

text: of

text: one

text: because

text: only

text: one

text: coordinate

text: is

text: needed

text: to

text: specify

text: point

text: on

text: itfor

text: example

text: the

text: point

text: at

text: on

text: number

text: line

text: surface

text: such

text: as

text: plane

text: or

text: the

text: surface

text: of

text: cylinder

text: or

text: sphere

text: has

text: dimension

text: of

text: two

text: because

text: two

text: coordinates

text: are

text: needed

text: to

text: specify

text: point

text: on

text: itfor

text: example

text: both

text: latitude

text: and

text: longitude

text: are

text: required

text: to

text: locate

text: point

text: on

text: the

text: surface

text: of

text: sphere

text: The

text: inside

text: of

text: cube

text: cylinder

text: or

text: sphere

text: is

text: three

text: dimensional

text: because

text: three

text: coordinates

text: are

text: needed

text: to

text: locate

text: point

text: within

text: these

text: spaces

text: In mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. An example of a polynomial of a single indeterminate is . An example in three variables is .

text: In

text: mathematics

text: polynomial

text: is

text: an

text: expression

text: consisting

text: of

text: variables

text: or

text: indeterminates

text: and

text: coefficients

text: that

text: involves

text: only

text: the

text: operations

text: of

text: addition

text: subtraction

text: multiplication

text: and

text: non

text: negative

text: integer

text: exponents

text: An

text: example

text: of

text: polynomial

text: of

text: single

text: indeterminate

text: is

text: An

text: example

text: in

text: three

text: variables

text: is

text: Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept).

text: Area

text: is

text: the

text: quantity

text: that

text: expresses

text: the

text: extent

text: of

text: two

text: dimensional

text: figure

text: or

text: shape

text: or

text: planar

text: lamina

text: in

text: the

text: plane

text: Surface

text: area

text: is

text: its

text: analog

text: on

text: the

text: two

text: dimensional

text: surface

text: of

text: three

text: dimensional

text: object

text: Area

text: can

text: be

text: understood

text: as

text: the

text: amount

text: of

text: material

text: with

text: given

text: thickness

text: that

text: would

text: be

text: necessary

text: to

text: fashion

text: model

text: of

text: the

text: shape

text: or

text: the

text: amount

text: of

text: paint

text: necessary

text: to

text: cover

text: the

text: surface

text: with

text: single

text: coat

text: It

text: is

text: the

text: two

text: dimensional

text: analog

text: of

text: the

text: length

text: of

text: curve

text: one

text: dimensional

text: concept

text: or

text: the

text: volume

text: of

text: solid

text: three

text: dimensional

text: concept

text: In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions, categories that are similar in some ways, but different in others. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not hold generally for real analytic functions. A function is analytic if and only if its Taylor series about "x" converges to the function in some neighborhood for every "x" in its domain.

text: In

text: mathematics

text: an

text: analytic

text: function

text: is

text: function

text: that

text: is

text: locally

text: given

text: by

text: convergent

text: power

text: series

text: There

text: exist

text: both

text: real

text: analytic

text: functions

text: and

text: complex

text: analytic

text: functions

text: categories

text: that

text: are

text: similar

text: in

text: some

text: ways

text: but

text: different

text: in

text: others

text: Functions

text: of

text: each

text: type

text: are

text: infinitely

text: differentiable

text: but

text: complex

text: analytic

text: functions

text: exhibit

text: properties

text: that

text: do

text: not

text: hold

text: generally

text: for

text: real

text: analytic

text: functions

text: function

text: is

text: analytic

text: if

text: and

text: only

text: if

text: its

text: Taylor

text: series

text: about

text: converges

text: to

text: the

text: function

text: in

text: some

text: neighborhood

text: for

text: every

text: in

text: its

text: domain

text: In mathematical analysis , a measure on a set is a systematic way to assign a number to each suitable subset of that set , intuitively interpreted as its size . In this sense , a measure is a generalization of the concepts of length , area , and volume . A particularly important example is the Lebesgue measure on a Euclidean space , which assigns the conventional length , area , and volume of Euclidean geometry to suitable subsets of the n - dimensional Euclidean space Rn . For instance , the Lebesgue measure of the interval ( 0 , 1 ) in the real numbers is its length in the everyday sense of the word -- specifically , 1 . Technically , a measure is a function that assigns a non-negative real number or +  to ( certain ) subsets of a set X ( see Definition below ) . It must assign 0 to the empty set and be ( countably ) additive : the measure of a ' large ' subset that can be decomposed into a finite ( or countable ) number of ' smaller ' disjoint subsets , is the sum of the measures of the `` smaller '' subsets . In general , if one wants to associate a consistent size to each subset of a given set while satisfying the other axioms of a measure , one only finds trivial examples like the counting measure . This problem was resolved by defining measure only on a sub-collection of all subsets ; the so - called measurable subsets , which are required to form a  - algebra . This means that countable unions , countable intersections and complements of measurable subsets are measurable . Non-measurable sets in a Euclidean space , on which the Lebesgue measure can not be defined consistently , are necessarily complicated in the sense of being badly mixed up with their complement . Indeed , their existence is a non-trivial consequence of the axiom of choice . Measure theory was developed in successive stages during the late 19th and early 20th centuries by Émile Borel , Henri Lebesgue , Johann Radon , and Maurice Fréchet , among others . The main applications of measures are in the foundations of the Lebesgue integral , in Andrey Kolmogorov 's axiomatisation of probability theory and in ergodic theory . In integration theory , specifying a measure allows one to define integrals on spaces more general than subsets of Euclidean space ; moreover , the integral with respect to the Lebesgue measure on Euclidean spaces is more general and has a richer theory than its predecessor , the Riemann integral . Probability theory considers measures that assign to the whole set the size 1 , and considers measurable subsets to be events whose probability is given by the measure . Ergodic theory considers measures that are invariant under , or arise naturally from , a dynamical system .

text: In

text: mathematical

text: analysis

text: measure

text: on

text: set

text: is

text: systematic

text: way

text: to

text: assign

text: number

text: to

text: each

text: suitable

text: subset

text: of

text: that

text: set

text: intuitively

text: interpreted

text: as

text: its

text: size

text: In

text: this

text: sense

text: measure

text: is

text: generalization

text: of

text: the

text: concepts

text: of

text: length

text: area

text: and

text: volume

text: particularly

text: important

text: example

text: is

text: the

text: Lebesgue

text: measure

text: on

text: Euclidean

text: space

text: which

text: assigns

text: the

text: conventional

text: length

text: area

text: and

text: volume

text: of

text: Euclidean

text: geometry

text: to

text: suitable

text: subsets

text: of

text: the

text: dimensional

text: Euclidean

text: space

text: Rn

text: For

text: instance

text: the

text: Lebesgue

text: measure

text: of

text: the

text: interval

text: in

text: the

text: real

text: numbers

text: is

text: its

text: length

text: in

text: the

text: everyday

text: sense

text: of

text: the

text: word

text: specifically

text: Technically

text: measure

text: is

text: function

text: that

text: assigns

text: non

text: negative

text: real

text: number

text: or

text: to

text: certain

text: subsets

text: of

text: set

text: see

text: Definition

text: below

text: It

text: must

text: assign

text: to

text: the

text: empty

text: set

text: and

text: be

text: countably

text: additive

text: the

text: measure

text: of

text: large

text: subset

text: that

text: can

text: be

text: decomposed

text: into

text: finite

text: or

text: countable

text: number

text: of

text: smaller

text: disjoint

text: subsets

text: is

text: the

text: sum

text: of

text: the

text: measures

text: of

text: the

text: smaller

text: subsets

text: In

text: general

text: if

text: one

text: wants

text: to

text: associate

text: consistent

text: size

text: to

text: each

text: subset

text: of

text: given

text: set

text: while

text: satisfying

text: the

text: other

text: axioms

text: of

text: measure

text: one

text: only

text: finds

text: trivial

text: examples

text: like

text: the

text: counting

text: measure

text: This

text: problem

text: was

text: resolved

text: by

text: defining

text: measure

text: only

text: on

text: sub

text: collection

text: of

text: all

text: subsets

text: the

text: so

text: called

text: measurable

text: subsets

text: which

text: are

text: required

text: to

text: form

text: algebra

text: This

text: means

text: that

text: countable

text: unions

text: countable

text: intersections

text: and

text: complements

text: of

text: measurable

text: subsets

text: are

text: measurable

text: Non

text: measurable

text: sets

text: in

text: Euclidean

text: space

text: on

text: which

text: the

text: Lebesgue

text: measure

text: can

text: not

text: be

text: defined

text: consistently

text: are

text: necessarily

text: complicated

text: in

text: the

text: sense

text: of

text: being

text: badly

text: mixed

text: up

text: with

text: their

text: complement

text: Indeed

text: their

text: existence

text: is

text: non

text: trivial

text: consequence

text: of

text: the

text: axiom

text: of

text: choice

text: Measure

text: theory

text: was

text: developed

text: in

text: successive

text: stages

text: during

text: the

text: late

text: and

text: early

text: centuries

text: by

text: Émile

text: Borel

text: Henri

text: Lebesgue

text: Johann

text: Radon

text: and

text: Maurice

text: Fréchet

text: among

text: others

text: The

text: main

text: applications

text: of

text: measures

text: are

text: in

text: the

text: foundations

text: of

text: the

text: Lebesgue

text: integral

text: in

text: Andrey

text: Kolmogorov

text: 's

text: axiomatisation

text: of

text: probability

text: theory

text: and

text: in

text: ergodic

text: theory

text: In

text: integration

text: theory

text: specifying

text: measure

text: allows

text: one

text: to

text: define

text: integrals

text: on

text: spaces

text: more

text: general

text: than

text: subsets

text: of

text: Euclidean

text: space

text: moreover

text: the

text: integral

text: with

text: respect

text: to

text: the

text: Lebesgue

text: measure

text: on

text: Euclidean

text: spaces

text: is

text: more

text: general

text: and

text: has

text: richer

text: theory

text: than

text: its

text: predecessor

text: the

text: Riemann

text: integral

text: Probability

text: theory

text: considers

text: measures

text: that

text: assign

text: to

text: the

text: whole

text: set

text: the

text: size

text: and

text: considers

text: measurable

text: subsets

text: to

text: be

text: events

text: whose

text: probability

text: is

text: given

text: by

text: the

text: measure

text: Ergodic

text: theory

text: considers

text: measures

text: that

text: are

text: invariant

text: under

text: or

text: arise

text: naturally

text: from

text: dynamical

text: system

text: Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the "Elements". Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. The "Elements" begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the "Elements" states results of what are now called algebra and number theory, explained in geometrical language.

text: Euclidean

text: geometry

text: is

text: mathematical

text: system

text: attributed

text: to

text: the

text: Alexandrian

text: Greek

text: mathematician

text: Euclid

text: which

text: he

text: described

text: in

text: his

text: textbook

text: on

text: geometry

text: the

text: Elements

text: Euclid

text: 's

text: method

text: consists

text: in

text: assuming

text: small

text: set

text: of

text: intuitively

text: appealing

text: axioms

text: and

text: deducing

text: many

text: other

text: propositions

text: theorems

text: from

text: these

text: Although

text: many

text: of

text: Euclid

text: 's

text: results

text: had

text: been

text: stated

text: by

text: earlier

text: mathematicians

text: Euclid

text: was

text: the

text: first

text: to

text: show

text: how

text: these

text: propositions

text: could

text: fit

text: into

text: comprehensive

text: deductive

text: and

text: logical

text: system

text: The

text: Elements

text: begins

text: with

text: plane

text: geometry

text: still

text: taught

text: in

text: secondary

text: school

text: as

text: the

text: first

text: axiomatic

text: system

text: and

text: the

text: first

text: examples

text: of

text: formal

text: proof

text: It

text: goes

text: on

text: to

text: the

text: solid

text: geometry

text: of

text: three

text: dimensions

text: Much

text: of

text: the

text: Elements

text: states

text: results

text: of

text: what

text: are

text: now

text: called

text: algebra

text: and

text: number

text: theory

text: explained

text: in

text: geometrical

text: language

text: A secondary school, often referred to as a high school or a senior high school, is a school which provides secondary education, between the ages of 11 and 19 depending on location, after primary school and before higher education.

text: secondary

text: school

text: often

text: referred

text: to

text: as

text: high

text: school

text: or

text: senior

text: high

text: school

text: is

text: school

text: which

text: provides

text: secondary

text: education

text: between

text: the

text: ages

text: of

text: and

text: depending

text: on

text: location

text: after

text: primary

text: school

text: and

text: before

text: higher

text: education

text: Alexandria (or ; Arabic: '; '; "") is the second largest city and a major economic centre in Egypt, extending about along the coast of the Mediterranean Sea in the north central part of the country. Its low elevation on the Nile delta makes it highly vulnerable to rising sea levels. Alexandria is Egypt's largest seaport, serving approximately 80% of Egypt's imports and exports. It is an important industrial center because of its natural gas and oil pipelines from Suez. Alexandria is also an important tourist destination.

text: Alexandria

text: or

text: Arabic

text: is

text: the

text: second

text: largest

text: city

text: and

text: major

text: economic

text: centre

text: in

text: Egypt

text: extending

text: about

text: along

text: the

text: coast

text: of

text: the

text: Mediterranean

text: Sea

text: in

text: the

text: north

text: central

text: part

text: of

text: the

text: country

text: Its

text: low

text: elevation

text: on

text: the

text: Nile

text: delta

text: makes

text: it

text: highly

text: vulnerable

text: to

text: rising

text: sea

text: levels

text: Alexandria

text: is

text: Egypt

text: 's

text: largest

text: seaport

text: serving

text: approximately

text: of

text: Egypt

text: 's

text: imports

text: and

text: exports

text: It

text: is

text: an

text: important

text: industrial

text: center

text: because

text: of

text: its

text: natural

text: gas

text: and

text: oil

text: pipelines

text: from

text: Suez

text: Alexandria

text: is

text: also

text: an

text: important

text: tourist

text: destination

text: Mathematics (from Greek  "máthma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.

text: Mathematics

text: from

text: Greek

text: máthma

text: knowledge

text: study

text: learning

text: is

text: the

text: study

text: of

text: topics

text: such

text: as

text: quantity

text: numbers

text: structure

text: space

text: and

text: change

text: There

text: is

text: range

text: of

text: views

text: among

text: mathematicians

text: and

text: philosophers

text: as

text: to

text: the

text: exact

text: scope

text: and

text: definition

text: of

text: mathematics

text: In mathematics, a planar lamina is a closed set in a plane of mass formula_1 and surface density formula_2 such that:

text: In

text: mathematics

text: planar

text: lamina

text: is

text: closed

text: set

text: in

text: plane

text: of

text: mass

text: and

text: surface

text: density

text: such

text: that

text: In mathematics, a theorem is a statement that has been proved on the basis of previously established statements, such as other theoremsand generally accepted statements, such as axioms. A theorem is a logical consequence of the axioms. The proof of a mathematical theorem is a logical argument for the theorem statement given in accord with the rules of a deductive system. The proof of a theorem is often interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally "deductive", in contrast to the notion of a scientific law, which is "experimental".

text: In

text: mathematics

text: theorem

text: is

text: statement

text: that

text: has

text: been

text: proved

text: on

text: the

text: basis

text: of

text: previously

text: established

text: statements

text: such

text: as

text: other

text: theoremsand

text: generally

text: accepted

text: statements

text: such

text: as

text: axioms

text: theorem

text: is

text: logical

text: consequence

text: of

text: the

text: axioms

text: The

text: proof

text: of

text: mathematical

text: theorem

text: is

text: logical

text: argument

text: for

text: the

text: theorem

text: statement

text: given

text: in

text: accord

text: with

text: the

text: rules

text: of

text: deductive

text: system

text: The

text: proof

text: of

text: theorem

text: is

text: often

text: interpreted

text: as

text: justification

text: of

text: the

text: truth

text: of

text: the

text: theorem

text: statement

text: In

text: light

text: of

text: the

text: requirement

text: that

text: theorems

text: be

text: proved

text: the

text: concept

text: of

text: theorem

text: is

text: fundamentally

text: deductive

text: in

text: contrast

text: to

text: the

text: notion

text: of

text: scientific

text: law

text: which

text: is

text: experimental

text: Henri Léon Lebesgue (June 28, 1875  July 26, 1941) was a French mathematician most famous for his theory of integration, which was a generalization of the 17th century concept of integrationsumming the area between an axis and the curve of a function defined for that axis. His theory was published originally in his dissertation "Intégrale, longueur, aire" ("Integral, length, area") at the University of Nancy during 1902.

text: Henri

text: Léon

text: Lebesgue

text: June

text: July

text: was

text: French

text: mathematician

text: most

text: famous

text: for

text: his

text: theory

text: of

text: integration

text: which

text: was

text: generalization

text: of

text: the

text: century

text: concept

text: of

text: integrationsumming

text: the

text: area

text: between

text: an

text: axis

text: and

text: the

text: curve

text: of

text: function

text: defined

text: for

text: that

text: axis

text: His

text: theory

text: was

text: published

text: originally

text: in

text: his

text: dissertation

text: Intégrale

text: longueur

text: aire

text: Integral

text: length

text: area

text: at

text: the

text: University

text: of

text: Nancy

text: during

annotations: follows single

question: part_of measure

answer: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics

text: mathematics


text:
Tuberculosis (TB) is an infectious disease caused by the bacterium "Mycobacterium tuberculosis" (MTB). Tuberculosis generally affects the lungs, but can also affect other parts of the body. Most infections do not have symptoms; in which case it is known as latent tuberculosis. About 10% of latent infections progress to active disease which, if left untreated, kills about half of those infected. The classic symptoms of active TB are a chronic cough with blood-containing sputum, fever, night sweats, and weight loss. The historical term "consumption" came about due to the weight loss. Infection of other organs can cause a wide range of symptoms.
Tuberculosis is spread through the air when people who have active TB in their lungs cough, spit, speak, or sneeze. People with latent TB do not spread the disease. Active infection occurs more often in people with HIV/AIDS and in those who smoke. Diagnosis of active TB is based on chest X-rays, as well as microscopic examination and culture of body fluids. Diagnosis of latent TB relies on the tuberculin skin test (TST) or blood tests.
Prevention of TB involves screening those at high risk, early detection and treatment of cases, and vaccination with the bacillus Calmette-Guérin vaccine. Those at high risk include household, workplace, and social contacts of people with active TB. Treatment requires the use of multiple antibiotics over a long period of time. Antibiotic resistance is a growing problem with increasing rates of multiple drug-resistant tuberculosis (MDR-TB).
One-third of the world's population is thought to be infected with TB. New infections occur in about 1% of the population each year. In 2014, there were 9.6 million cases of active TB which resulted in 1.5 million deaths. More than 95% of deaths occurred in developing countries. The number of new cases each year has decreased since 2000. About 80% of people in many Asian and African countries test positive while 510% of people in the United States population tests positive by the tuberculin test. Tuberculosis has been present in humans since ancient times.

text: Tuberculosis

text: TB

text: is

text: an

text: infectious

text: disease

text: caused

text: by

text: the

text: bacterium

text: Mycobacterium

text: tuberculosis

text: MTB

text: Tuberculosis

text: generally

text: affects

text: the

text: lungs

text: but

text: can

text: also

text: affect

text: other

text: parts

text: of

text: the

text: body

text: Most

text: infections

text: do

text: not

text: have

text: symptoms

text: in

text: which

text: case

text: it

text: is

text: known

text: as

text: latent

text: tuberculosis

text: About

text: of

text: latent

text: infections

text: progress

text: to

text: active

text: disease

text: which

text: if

text: left

text: untreated

text: kills

text: about

text: half

text: of

text: those

text: infected

text: The

text: classic

text: symptoms

text: of

text: active

text: TB

text: are

text: chronic

text: cough

text: with

text: blood

text: containing

text: sputum

text: fever

text: night

text: sweats

text: and

text: weight

text: loss

text: The

text: historical

text: term

text: consumption

text: came

text: about

text: due

text: to

text: the

text: weight

text: loss

text: Infection

text: of

text: other

text: organs

text: can

text: cause

text: wide

text: range

text: of

text: symptoms

text: Tuberculosis

text: is

text: spread

text: through

text: the

text: air

text: when

text: people

text: who

text: have

text: active

text: TB

text: in

text: their

text: lungs

text: cough

text: spit

text: speak

text: or

text: sneeze

text: People

text: with

text: latent

text: TB

text: do

text: not

text: spread

text: the

text: disease

text: Active

text: infection

text: occurs

text: more

text: often

text: in

text: people

text: with

text: HIV

text: AIDS

text: and

text: in

text: those

text: who

text: smoke

text: Diagnosis

text: of

text: active

text: TB

text: is

text: based

text: on

text: chest

text: rays

text: as

text: well

text: as

text: microscopic

text: examination

text: and

text: culture

text: of

text: body

text: fluids

text: Diagnosis

text: of

text: latent

text: TB

text: relies

text: on

text: the

text: tuberculin

text: skin

text: test

text: TST

text: or

text: blood

text: tests

text: Prevention

text: of

text: TB

text: involves

text: screening

text: those

text: at

text: high

text: risk

text: early

text: detection

text: and

text: treatment

text: of

text: cases

text: and

text: vaccination

text: with

text: the

text: bacillus

text: Calmette

text: Guérin

text: vaccine

text: Those

text: at

text: high

text: risk

text: include

text: household

text: workplace

text: and

text: social

text: contacts

text: of

text: people

text: with

text: active

text: TB

text: Treatment

text: requires

text: the

text: use

text: of

text: multiple

text: antibiotics

text: over

text: long

text: period

text: of

text: time

text: Antibiotic

text: resistance

text: is

text: growing

text: problem

text: with

text: increasing

text: rates

text: of

text: multiple

text: drug

text: resistant

text: tuberculosis

text: MDR

text: TB

text: One

text: third

text: of

text: the

text: world

text: 's

text: population

text: is

text: thought

text: to

text: be

text: infected

text: with

text: TB

text: New

text: infections

text: occur

text: in

text: about

text: of

text: the

text: population

text: each

text: year

text: In

text: there

text: were

text: million

text: cases

text: of

text: active

text: TB

text: which

text: resulted

text: in

text: million

text: deaths

text: More

text: than

text: of

text: deaths

text: occurred

text: in

text: developing

text: countries

text: The

text: number

text: of

text: new

text: cases

text: each

text: year

text: has

text: decreased

text: since

text: About

text: of

text: people

text: in

text: many

text: Asian

text: and

text: African

text: countries

text: test

text: positive

text: while

text: of

text: people

text: in

text: the

text: United

text: States

text: population

text: tests

text: positive

text: by

text: the

text: tuberculin

text: test

text: Tuberculosis

text: has

text: been

text: present

text: in

text: humans

text: since

text: ancient

text: times

text: A lymph node or lymph gland, is an ovoid or kidney-shaped organ of the lymphatic system, and of the adaptive immune system, that is widely present throughout the body. They are linked by the lymphatic vessels as a part of the circulatory system. Lymph nodes are major sites of B and T lymphocytes, and other white blood cells. Lymph nodes are important for the proper functioning of the immune system, acting as filters for foreign particles and cancer cells. Lymph nodes do not have a detoxification function, which is primarily dealt with by the liver and kidneys.

text: lymph

text: node

text: or

text: lymph

text: gland

text: is

text: an

text: ovoid

text: or

text: kidney

text: shaped

text: organ

text: of

text: the

text: lymphatic

text: system

text: and

text: of

text: the

text: adaptive

text: immune

text: system

text: that

text: is

text: widely

text: present

text: throughout

text: the

text: body

text: They

text: are

text: linked

text: by

text: the

text: lymphatic

text: vessels

text: as

text: part

text: of

text: the

text: circulatory

text: system

text: Lymph

text: nodes

text: are

text: major

text: sites

text: of

text: and

text: lymphocytes

text: and

text: other

text: white

text: blood

text: cells

text: Lymph

text: nodes

text: are

text: important

text: for

text: the

text: proper

text: functioning

text: of

text: the

text: immune

text: system

text: acting

text: as

text: filters

text: for

text: foreign

text: particles

text: and

text: cancer

text: cells

text: Lymph

text: nodes

text: do

text: not

text: have

text: detoxification

text: function

text: which

text: is

text: primarily

text: dealt

text: with

text: by

text: the

text: liver

text: and

text: kidneys

text: A diagnosis of latent tuberculosis (LTB), also called latent tuberculosis infection (LTBI) means a patient is infected with "Mycobacterium tuberculosis", but the patient does not have active tuberculosis. Active tuberculosis can be contagious while latent tuberculosis is not, and it is therefore not possible to get TB from someone with latent tuberculosis. The main risk is that approximately 10% of these patients (5% in the first two years after infection and 0.1% per year thereafter) will go on to develop active tuberculosis. This is particularly true, and there is added risk, in particular situations such as medication that suppresses the immune system or advancing age.

text: diagnosis

text: of

text: latent

text: tuberculosis

text: LTB

text: also

text: called

text: latent

text: tuberculosis

text: infection

text: LTBI

text: means

text: patient

text: is

text: infected

text: with

text: Mycobacterium

text: tuberculosis

text: but

text: the

text: patient

text: does

text: not

text: have

text: active

text: tuberculosis

text: Active

text: tuberculosis

text: can

text: be

text: contagious

text: while

text: latent

text: tuberculosis

text: is

text: not

text: and

text: it

text: is

text: therefore

text: not

text: possible

text: to

text: get

text: TB

text: from

text: someone

text: with

text: latent

text: tuberculosis

text: The

text: main

text: risk

text: is

text: that

text: approximately

text: of

text: these

text: patients

text: in

text: the

text: first

text: two

text: years

text: after

text: infection

text: and

text: per

text: year

text: thereafter

text: will

text: go

text: on

text: to

text: develop

text: active

text: tuberculosis

text: This

text: is

text: particularly

text: true

text: and

text: there

text: is

text: added

text: risk

text: in

text: particular

text: situations

text: such

text: as

text: medication

text: that

text: suppresses

text: the

text: immune

text: system

text: or

text: advancing

text: age

text: Mycobacterial cervical lymphadenitis , also known as scrofula or King 's evil , refers to a lymphadenitis of the cervical lymph nodes associated with tuberculosis as well as non-tuberculous ( atypical ) mycobacteria .

text: Mycobacterial

text: cervical

text: lymphadenitis

text: also

text: known

text: as

text: scrofula

text: or

text: King

text: 's

text: evil

text: refers

text: to

text: lymphadenitis

text: of

text: the

text: cervical

text: lymph

text: nodes

text: associated

text: with

text: tuberculosis

text: as

text: well

text: as

text: non

text: tuberculous

text: atypical

text: mycobacteria

text: A vaccine is a biological preparation that provides active acquired immunity to a particular disease. A vaccine typically contains an agent that resembles a disease-causing microorganism and is often made from weakened or killed forms of the microbe, its toxins or one of its surface proteins. The agent stimulates the body's immune system to recognize the agent as a threat, destroy it, and keep a record of it so that the immune system can more easily recognize and destroy any of these microorganisms that it later encounters. Vaccines can be prophylactic (example: to prevent or ameliorate the effects of a future infection by any natural or "wild" pathogen), or therapeutic (e.g., vaccines against cancer are being investigated).

text: vaccine

text: is

text: biological

text: preparation

text: that

text: provides

text: active

text: acquired

text: immunity

text: to

text: particular

text: disease

text: vaccine

text: typically

text: contains

text: an

text: agent

text: that

text: resembles

text: disease

text: causing

text: microorganism

text: and

text: is

text: often

text: made

text: from

text: weakened

text: or

text: killed

text: forms

text: of

text: the

text: microbe

text: its

text: toxins

text: or

text: one

text: of

text: its

text: surface

text: proteins

text: The

text: agent

text: stimulates

text: the

text: body

text: 's

text: immune

text: system

text: to

text: recognize

text: the

text: agent

text: as

text: threat

text: destroy

text: it

text: and

text: keep

text: record

text: of

text: it

text: so

text: that

text: the

text: immune

text: system

text: can

text: more

text: easily

text: recognize

text: and

text: destroy

text: any

text: of

text: these

text: microorganisms

text: that

text: it

text: later

text: encounters

text: Vaccines

text: can

text: be

text: prophylactic

text: example

text: to

text: prevent

text: or

text: ameliorate

text: the

text: effects

text: of

text: future

text: infection

text: by

text: any

text: natural

text: or

text: wild

text: pathogen

text: or

text: therapeutic

text: e.g.

text: vaccines

text: against

text: cancer

text: are

text: being

text: investigated

text: Vaccination is the administration of antigenic material (a vaccine) to stimulate an individual's immune system to develop adaptive immunity to a pathogen. Vaccines can prevent or ameliorate morbidity from infection. When a sufficiently large percentage of a population has been vaccinated, this results in herd immunity. The effectiveness of vaccination has been widely studied and verified; for example, the influenza vaccine, the HPV vaccine, and the chicken pox vaccine. Vaccination is the most effective method of preventing infectious diseases; widespread immunity due to vaccination is largely responsible for the worldwide eradication of smallpox and the restriction of diseases such as polio, measles, and tetanus from much of the world. The World Health Organization (WHO) reports that licensed vaccines are currently available to prevent or contribute to the prevention and control of twenty-five preventable infections.

text: Vaccination

text: is

text: the

text: administration

text: of

text: antigenic

text: material

text: vaccine

text: to

text: stimulate

text: an

text: individual

text: 's

text: immune

text: system

text: to

text: develop

text: adaptive

text: immunity

text: to

text: pathogen

text: Vaccines

text: can

text: prevent

text: or

text: ameliorate

text: morbidity

text: from

text: infection

text: When

text: sufficiently

text: large

text: percentage

text: of

text: population

text: has

text: been

text: vaccinated

text: this

text: results

text: in

text: herd

text: immunity

text: The

text: effectiveness

text: of

text: vaccination

text: has

text: been

text: widely

text: studied

text: and

text: verified

text: for

text: example

text: the

text: influenza

text: vaccine

text: the

text: HPV

text: vaccine

text: and

text: the

text: chicken

text: pox

text: vaccine

text: Vaccination

text: is

text: the

text: most

text: effective

text: method

text: of

text: preventing

text: infectious

text: diseases

text: widespread

text: immunity

text: due

text: to

text: vaccination

text: is

text: largely

text: responsible

text: for

text: the

text: worldwide

text: eradication

text: of

text: smallpox

text: and

text: the

text: restriction

text: of

text: diseases

text: such

text: as

text: polio

text: measles

text: and

text: tetanus

text: from

text: much

text: of

text: the

text: world

text: The

text: World

text: Health

text: Organization

text: WHO

text: reports

text: that

text: licensed

text: vaccines

text: are

text: currently

text: available

text: to

text: prevent

text: or

text: contribute

text: to

text: the

text: prevention

text: and

text: control

text: of

text: twenty

text: five

text: preventable

text: infections

text:
Human immunodeficiency virus infection and acquired immune deficiency syndrome (HIV/AIDS) is a spectrum of conditions caused by infection with the human immunodeficiency virus (HIV). Following initial infection, a person may not notice any symptoms or may experience a brief period of influenza-like illness. Typically, this is followed by a prolonged period with no symptoms. As the infection progresses, it interferes more with the immune system, increasing the risk of common infections like tuberculosis, as well as other opportunistic infections, and tumors that rarely affect people who have working immune systems. These late symptoms of infection are referred to as AIDS. This stage is often also associated with weight loss.
HIV is spread primarily by unprotected sex (including anal and oral sex), contaminated blood transfusions, hypodermic needles, and from mother to child during pregnancy, delivery, or breastfeeding. Some bodily fluids, such as saliva and tears, do not transmit HIV. Methods of prevention include safe sex, needle exchange programs, treating those who are infected, and male circumcision. Disease in a baby can often be prevented by giving both the mother and child antiretroviral medication. There is no cure or vaccine; however, antiretroviral treatment can slow the course of the disease and may lead to a near-normal life expectancy. Treatment is recommended as soon as the diagnosis is made. Without treatment, the average survival time after infection is 11 years.
In 2015 about 36.7 million people were living with HIV and it resulted in 1.1 million deaths. Most of those infected live in sub-Saharan Africa. Between its discovery and 2014 AIDS has caused an estimated 39 million deaths worldwide. HIV/AIDS is considered a pandemica disease outbreak which is present over a large area and is actively spreading. HIV is believed to have originated in west-central Africa during the late 19th or early 20th century. AIDS was first recognized by the United States Centers for Disease Control and Prevention (CDC) in 1981 and its causeHIV infectionwas identified in the early part of the decade.
HIV/AIDS has had a great impact on society, both as an illness and as a source of discrimination. The disease also has large economic impacts. There are many misconceptions about HIV/AIDS such as the belief that it can be transmitted by casual non-sexual contact. The disease has become subject to many controversies involving religion including the Catholic Church's decision not to support condom use as prevention. It has attracted international medical and political attention as well as large-scale funding since it was identified in the 1980s.

text: Human

text: immunodeficiency

text: virus

text: infection

text: and

text: acquired

text: immune

text: deficiency

text: syndrome

text: HIV

text: AIDS

text: is

text: spectrum

text: of

text: conditions

text: caused

text: by

text: infection

text: with

text: the

text: human

text: immunodeficiency

text: virus

text: HIV

text: Following

text: initial

text: infection

text: person

text: may

text: not

text: notice

text: any

text: symptoms

text: or

text: may

text: experience

text: brief

text: period

text: of

text: influenza

text: like

text: illness

text: Typically

text: this

text: is

text: followed

text: by

text: prolonged

text: period

text: with

text: no

text: symptoms

text: As

text: the

text: infection

text: progresses

text: it

text: interferes

text: more

text: with

text: the

text: immune

text: system

text: increasing

text: the

text: risk

text: of

text: common

text: infections

text: like

text: tuberculosis

text: as

text: well

text: as

text: other

text: opportunistic

text: infections

text: and

text: tumors

text: that

text: rarely

text: affect

text: people

text: who

text: have

text: working

text: immune

text: systems

text: These

text: late

text: symptoms

text: of

text: infection

text: are

text: referred

text: to

text: as

text: AIDS

text: This

text: stage

text: is

text: often

text: also

text: associated

text: with

text: weight

text: loss

text: HIV

text: is

text: spread

text: primarily

text: by

text: unprotected

text: sex

text: including

text: anal

text: and

text: oral

text: sex

text: contaminated

text: blood

text: transfusions

text: hypodermic

text: needles

text: and

text: from

text: mother

text: to

text: child

text: during

text: pregnancy

text: delivery

text: or

text: breastfeeding

text: Some

text: bodily

text: fluids

text: such

text: as

text: saliva

text: and

text: tears

text: do

text: not

text: transmit

text: HIV

text: Methods

text: of

text: prevention

text: include

text: safe

text: sex

text: needle

text: exchange

text: programs

text: treating

text: those

text: who

text: are

text: infected

text: and

text: male

text: circumcision

text: Disease

text: in

text: baby

text: can

text: often

text: be

text: prevented

text: by

text: giving

text: both

text: the

text: mother

text: and

text: child

text: antiretroviral

text: medication

text: There

text: is

text: no

text: cure

text: or

text: vaccine

text: however

text: antiretroviral

text: treatment

text: can

text: slow

text: the

text: course

text: of

text: the

text: disease

text: and

text: may

text: lead

text: to

text: near

text: normal

text: life

text: expectancy

text: Treatment

text: is

text: recommended

text: as

text: soon

text: as

text: the

text: diagnosis

text: is

text: made

text: Without

text: treatment

text: the

text: average

text: survival

text: time

text: after

text: infection

text: is

text: years

text: In

text: about

text: million

text: people

text: were

text: living

text: with

text: HIV

text: and

text: it

text: resulted

text: in

text: million

text: deaths

text: Most

text: of

text: those

text: infected

text: live

text: in

text: sub

text: Saharan

text: Africa

text: Between

text: its

text: discovery

text: and

text: AIDS

text: has

text: caused

text: an

text: estimated

text: million

text: deaths

text: worldwide

text: HIV

text: AIDS

text: is

text: considered

text: pandemica

text: disease

text: outbreak

text: which

text: is

text: present

text: over

text: large

text: area

text: and

text: is

text: actively

text: spreading

text: HIV

text: is

text: believed

text: to

text: have

text: originated

text: in

text: west

text: central

text: Africa

text: during

text: the

text: late

text: or

text: early

text: century

text: AIDS

text: was

text: first

text: recognized

text: by

text: the

text: United

text: States

text: Centers

text: for

text: Disease

text: Control

text: and

text: Prevention

text: CDC

text: in

text: and

text: its

text: causeHIV

text: infectionwas

text: identified

text: in

text: the

text: early

text: part

text: of

text: the

text: decade

text: HIV

text: AIDS

text: has

text: had

text: great

text: impact

text: on

text: society

text: both

text: as

text: an

text: illness

text: and

text: as

text: source

text: of

text: discrimination

text: The

text: disease

text: also

text: has

text: large

text: economic

text: impacts

text: There

text: are

text: many

text: misconceptions

text: about

text: HIV

text: AIDS

text: such

text: as

text: the

text: belief

text: that

text: it

text: can

text: be

text: transmitted

text: by

text: casual

text: non

text: sexual

text: contact

text: The

text: disease

text: has

text: become

text: subject

text: to

text: many

text: controversies

text: involving

text: religion

text: including

text: the

text: Catholic

text: Church

text: 's

text: decision

text: not

text: to

text: support

text: condom

text: use

text: as

text: prevention

text: It

text: has

text: attracted

text: international

text: medical

text: and

text: political

text: attention

text: as

text: well

text: as

text: large

text: scale

text: funding

text: since

text: it

text: was

text: identified

text: in

text: the

text: Sputum is mucus and is the name used for the coughed-up material (phlegm) from the lower airways (trachea and bronchi). This process is known as sputilization. In medicine, sputum samples are usually used for naked eye exam, microbiological investigations of respiratory infections and cytological investigations of respiratory systems. It is critical that the patient not give a specimen that includes any mucoid material from the interior of the nose. Naked eye exam of sputum can be done at home by a patient in order to note the various colors (see below). Any hint of yellow color suggests an airway infection (but does not indicate between the types of organisms causing it). Such color hints are best detected when the sputum is viewed on a very white background such as white paper, a white pot, or a white sink surface. The more intense the yellow color, the more likely it is a bacterial infection (bronchitis, bronchopneumonia, or pneumonia).

text: Sputum

text: is

text: mucus

text: and

text: is

text: the

text: name

text: used

text: for

text: the

text: coughed

text: up

text: material

text: phlegm

text: from

text: the

text: lower

text: airways

text: trachea

text: and

text: bronchi

text: This

text: process

text: is

text: known

text: as

text: sputilization

text: In

text: medicine

text: sputum

text: samples

text: are

text: usually

text: used

text: for

text: naked

text: eye

text: exam

text: microbiological

text: investigations

text: of

text: respiratory

text: infections

text: and

text: cytological

text: investigations

text: of

text: respiratory

text: systems

text: It

text: is

text: critical

text: that

text: the

text: patient

text: not

text: give

text: specimen

text: that

text: includes

text: any

text: mucoid

text: material

text: from

text: the

text: interior

text: of

text: the

text: nose

text: Naked

text: eye

text: exam

text: of

text: sputum

text: can

text: be

text: done

text: at

text: home

text: by

text: patient

text: in

text: order

text: to

text: note

text: the

text: various

text: colors

text: see

text: below

text: Any

text: hint

text: of

text: yellow

text: color

text: suggests

text: an

text: airway

text: infection

text: but

text: does

text: not

text: indicate

text: between

text: the

text: types

text: of

text: organisms

text: causing

text: it

text: Such

text: color

text: hints

text: are

text: best

text: detected

text: when

text: the

text: sputum

text: is

text: viewed

text: on

text: very

text: white

text: background

text: such

text: as

text: white

text: paper

text: white

text: pot

text: or

text: white

text: sink

text: surface

text: The

text: more

text: intense

text: the

text: yellow

text: color

text: the

text: more

text: likely

text: it

text: is

text: bacterial

text: infection

text: bronchitis

text: bronchopneumonia

text: or

text: pneumonia

text: White blood cells (WBCs), also called leukocytes or leucocytes, are the cells of the immune system that are involved in protecting the body against both infectious disease and foreign invaders. All white blood cells are produced and derived from multipotent cells in the bone marrow known as hematopoietic stem cells. Leukocytes are found throughout the body, including the blood and lymphatic system.

text: White

text: blood

text: cells

text: WBCs

text: also

text: called

text: leukocytes

text: or

text: leucocytes

text: are

text: the

text: cells

text: of

text: the

text: immune

text: system

text: that

text: are

text: involved

text: in

text: protecting

text: the

text: body

text: against

text: both

text: infectious

text: disease

text: and

text: foreign

text: invaders

text: All

text: white

text: blood

text: cells

text: are

text: produced

text: and

text: derived

text: from

text: multipotent

text: cells

text: in

text: the

text: bone

text: marrow

text: known

text: as

text: hematopoietic

text: stem

text: cells

text: Leukocytes

text: are

text: found

text: throughout

text: the

text: body

text: including

text: the

text: blood

text: and

text: lymphatic

text: system

annotations: follows multiple

question: medical_specialty tuberculous cervical lymphadenitis

answer: infectious disease

text: infectious disease

text: infectious disease