Irrational number

In mathematics, an irrational number is any real number that is not a rational number, i.e., one that cannot be written as a ratio of two integers, i.e., it is not of the form

[math]\displaystyle{ \Large \frac{a}{b} }[/math]

where a and b are integers and b is not zero. It can readily be shown that the irrational numbers are precisely those numbers whose expansion in any given base (decimal, binary, etc) never ends and never enters a periodic pattern, but no mathematician takes that to be a definition. Some examples of irrational numbers are [math]\displaystyle{ \sqrt{2} }[/math] or [math]\displaystyle{ e }[/math].

External links

• Irrational number

Number classes

General numbers

Integer Natural Even Odd Rational Irrational Real Prime Probable prime

Special numbers

Mersenne 2n-1 Fermat 22n+1 Proth k•2n+1 Riesel k•2n-1 Woodall n•2n-1 Cullen n•2n+1 Double Mersenne 22p-1-1 Perfect 2n-1(2n-1) Leyland xy ± yx Gen.Repunit (b^n-1)/(b-1)

Prime numbers

Mersenne Proth Riesel Williams (b±1)bn±1 Carol/Kynea (bn±1)2-2 Multifactorial n!j±1