Computable number

In mathematics, computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm. 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 Émile Borel in 1912, using the intuitive notion of computability available at the time.

Equivalent definitions can be given using μ-recursive functions, Turing machines, or λ-calculus as the formal representation of algorithms. The set of computable numbers is sometimes denoted by 𝕂. The idea of computable numbers can be further extended to computable complex numbers(or gaussian computable numbers) - whose both real and imaginary components are computable. The computable numbers form a real closed field and can be used in the place of real numbers for many, but not all, mathematical purposes.