Difference between revisions of "Irrational number"
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==Formulations== | ==Formulations== | ||
Revision as of 00:08, June 28, 2007
An irrational number is a number that cannot be expressed as the ratio of two integers. Irrational numbers together with rational numbers make up the set of real numbers.
Irrational numbers often arise as solutions to problems involoving rational numbers. For example, the square root of 2 is irrational. Other irrationals, such as pi, serve as fundamental constants in many mathematical problems.
Irrational numbers can never be expressed exactly using decimal notation. Instead it is common to write them using only enough significant digits to solve the problem at hand, followed by an elipsis:
- <math>\pi\ = 3.14159...</math>
Simply, an irrational number can be defined as a non-repeating and non-terminating number, usually a decimal.
Formulations
An irrational number is formally defined to be the limit of a cauchy sequence of rational numbers.