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单词 Irrational
释义

irrational


An irrational number is a real number which cannot be represented as a ratio of two integers. That is, if x is irrational, then

xab

with a,b and b0.

Examples

  1. 1.

    2p is irrational for p=2,3,,

  2. 2.

    π,e, and 2p for p=2,3,,are irrational,

  3. 3.

    It is not known whether Euler’s constant is rational or irrational.

Properties

  1. 1.

    It a is a real number and an is irrational for some n=2,3,,then a is irrational (proof (http://planetmath.org/IfAnIsIrrationalThenAIsIrrational)).

  2. 2.

    The sum, difference, product, and quotient (when defined) of two numbers,one rational and another irrational, is irrational.(proof (http://planetmath.org/RationalAndIrrational)).

Titleirrational
Canonical nameIrrational
Date of creation2013-03-22 11:55:59
Last modified on2013-03-22 11:55:59
Owneryark (2760)
Last modified byyark (2760)
Numerical id12
Authoryark (2760)
Entry typeDefinition
Classificationmsc 11J82
Classificationmsc 11J72
Synonymirrational number
Related topicTranscedentalNumber
Related topicAlgebraicNumber
Related topicInteger
Related topicLindemannWeierstrassTheorem
Related topicGelfondsTheorem
Related topicProofThatTheRationalsAreCountable
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更新时间:2025/5/4 23:42:51