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Difference between revisions of "Irrational number"
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| − | 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 | + | 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>\Large \frac{a}{b}</math> | :<math>\Large \frac{a}{b}</math> | ||
| − | where a and b are [[integer]]s 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>\sqrt{2}</math> or <math>e</math>. | + | where <math>a</math> and <math>b</math> are [[integer]]s and <math>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>\sqrt{2}</math> or <math>e</math>. |
==External links== | ==External links== | ||
| − | *[[Wikipedia:Irrational_number| | + | *[[Wikipedia:Irrational_number|Irrational number]] |
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{{Navbox NumberClasses}} | {{Navbox NumberClasses}} | ||
| − | [[Category: | + | |
| + | [[Category:Number systems]] | ||
Latest revision as of 15:14, 26 March 2023
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].
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Number classes
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