Over the centuries mathematicians have come to recognise that it's useful to talk about different types of number. These include:

As time has gone by, the usual number line has been extended, and we can also talk about:

CategoryMetaTopic
AGentleIntroductionToTimeComplexity
CountableSet
DifferenceOfTwoSquares
(none) FermatPrime
FermatNumber

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TypesOfNumber
AlgebraicNumber
CategoryMetaTopic
ComplexNumber
CountingNumber
ImaginaryNumber
Integer
IrrationalNumber
PerfectNumber
Quaternion
RationalNumber
RealNumber
TranscendentalNumber
WholeNumber
ArgandDiagram
CategoryMeta
CauchySequence
Commutative
ComplexConjugate
ComplexPlane
CompositeNumber
ContinuedFraction
CountableSet
CubeRoot
DedekindCut
Denominator
DividingComplexNumbers
Divisor
Euclid
Euler
MersennePrime
MultiplyingComplexNumbers
NaturalNumber
Numerator
PolarRepresentationOfAComplexNumber
Polynomial
PrimePair
Pythagoras
ReducingFractionsToLowestTerms
RootTwoIsIrrational
ScalarProduct
SquareRoot
Vectors