Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3).
Navigation
Topics Help • Register • News • History • How to • Sequences statistics • Template prototypes

Irrational number

From Prime-Wiki
Revision as of 15:14, 26 March 2023 by Happy5214 (talk | contribs) (Moving to new subcategory)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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 [math]\displaystyle{ a }[/math] and [math]\displaystyle{ b }[/math] are integers and [math]\displaystyle{ b }[/math] 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

Number classes
General numbers
Special numbers
Prime numbers