Difference between revisions of "Irrational number"

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(→‎See also: clean up & uniformity)
 
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An '''irrational number''' is a number that cannot be expressed as the ratio of two [[integers]].  Irrational numbers together with [[rational number]]s make up the set of [[real numbers]].
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An '''irrational number''' is a [[real number]] that cannot be expressed as the ratio of two [[integers]].  
  
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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.
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Irrational numbers often arise as solutions to problems involving 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 with a finite number of digits.  Instead it is common to write them using only enough significant digits to solve the problem at hand, followed by an ellipsis (…):
 
Irrational numbers can never be expressed exactly using decimal notation with a finite number of digits.  Instead it is common to write them using only enough significant digits to solve the problem at hand, followed by an ellipsis (…):
  
 
:<math>\pi\ = 3.1415926...</math>
 
:<math>\pi\ = 3.1415926...</math>
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Simply, an irrational number can be defined as a non-repeating and non-terminating number, usually a decimal.
 
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==Formulations==
 
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An irrational number is formally defined to be the limit of a [[Cauchy sequence]] of rational numbers.
 
  
 
==See also==
 
==See also==
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[[Transcendental numbers]]
 
[[Transcendental numbers]]
  
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[[Category:mathematics]]
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[[Category:Mathematics]]

Latest revision as of 14:27, July 13, 2016

An irrational number is a real number that cannot be expressed as the ratio of two integers.

Irrational numbers often arise as solutions to problems involving 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 with a finite number of digits. Instead it is common to write them using only enough significant digits to solve the problem at hand, followed by an ellipsis (…):

<math>\pi\ = 3.1415926...</math>

See also

Transcendental numbers