Computable number

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, computable numbers are the <a href="/facts/Real_number/R02gw5Pb">real numbers</a> that can be computed to within any desired precision by a finite, terminating <a href="/facts/Algorithm/fnl5NmRt">algorithm</a>. They are also known as the recursive numbers, effective numbers, computable reals, or recursive reals. The concept of a computable real number was introduced by <a href="/facts/%25C3%2589mile_Borel/lF9PBa1T">Émile Borel</a> in 1912, using the intuitive notion of computability available at the time.
</p><p>Equivalent definitions can be given using <a href="/facts/%25CE%259C-recursive_function/pQezUupS">μ-recursive functions</a>, <a href="/facts/Turing_machine/ojCtglYu">Turing machines</a>, or <a href="/facts/%25CE%259B-calculus/DaD3RuQ4">λ-calculus</a> as the formal representation of algorithms. The computable numbers form a <a href="/facts/Real_closed_field/Vj1Un2fw">real closed field</a> and can be used in the place of real numbers for many, but not all, mathematical purposes.
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Computable number open-in-new

Computable number