The "Real Numbers" are all the "locations" on the number line.

Interestingly, between every pair of rational numbers there are infinitely many irrational numbers, and between every pair of irrational numbers there are infinitely many rational numbers.
One way of dividing the real numbers is:

Rational numbers versus irrational numbers,

Algebraic numbers versus transcendental numbers.

The real numbers can be counter-intuitive.

The reals can be constructed via

Cauchy Sequences
Dedekind Cuts
Infinite decimal expansions
Continued Fractions

A4Paper ApproximatingPi Denominator DividingRationalNumbers ImproperFraction MultiplyingRationalNumbers Numerator PiIsIrrational ReducingFractionsToLowestTerms SubtractingRationalNumbers	CountableSet DiophantineEquation DividingWholeNumbers EIsIrrational Euclid EuclideanAlgorithm MixedNumber RootTwoIsIrrational			AGentleIntroductionToTimeComplexity AddingComplexNumbers Admin_NavigationBar AlgebraicTopology AssociativeOperation BasinOfAttraction BinaryRelation BirthdayProblem Calculus CantorSet CategoryMetaTopic ChainRule CoDomainOfAFunction CommonCoreDomains CommonFactor CommonMultiple CommutativeOperation CompositeNumber CountingNumber DifferentialCalculus EquationOfALine EulersNumber Factorial FactoringIntegers FactoringQuadratics FermatNumber FermatsLastTheorem FermatsLittleTheorem FrontPage GerolamoCardano HighestCommonFactor HolomorphicFunction HyperbolicFunction ImageOfAFunction IntegralCalculus IntegrationByParts InverseFunction IsaacNewton LeastCommonMultiple LinearFunction MagnitudeOfAComplexNumber ModuloArithmetic MultiplyingComplexNumbers MultiplyingFractions NamingPhilosophy NaturalLogarithm NaturalNumber NewtonRaphsonMethod OrdinaryDifferentialEquation PartialDifferentialEquation PerfectNumber Polynomial PrimeNumber PrimeNumberTheorem PythagorasTheorem RangeOfAFunction RationalisingTheDenominator RiemannSurface RiemannZetaFunction Root ScalarProduct SiteNavigation SquareNumber SuggestedReading Surd TransfiniteNumbers TrigonometricFunction UnitVector VectorSubtraction Vectors WhatIsATopic WholeNumber ZeroFactorial ZornsLemma
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AlgebraicNumber CauchySequence ContinuedFraction DedekindCut IrrationalNumber RationalNumber TranscendentalNumber			AbsoluteValue Adding2DVectors AddingRealNumbers AddingVectors ArgandDiagram ComplexConjugate ComplexNumber ComplexPlane ContinuumHypothesis CubeRoot DifferenceOfTwoSquares DividingComplexNumbers DividingRealNumbers Divisor DomainOfAFunction Function FundamentalTheoremOfAlgebra GeorgCantor ImaginaryNumber Integer Logarithm MagnitudeOfAVector MathematicsTaxonomy MultiplyingRealNumbers NewUserIntroduction NewtonsMethod PolarRepresentationOfAComplexNumber Quaternion RiemannHypothesis RootsOfPolynomials SquareRoot SubtractingRealNumbers TypesOfNumber UncountableSet
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		⇌	You are here RealNumber
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ComplexNumber CountableSet CubeRoot Denominator GeneralSequence Integer Numerator Polynomial Pythagoras ReducingFractionsToLowestTerms RootTwoIsIrrational SquareRoot WholeNumber	(none)			(none)

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