A noncomputable number is a real or complex number which cannot be approximated to arbitrary prescribed accuracy by an algorithm. In particular, a real number 
is computable if an algorithm, given
,
produces a rational number 
satisfying 
; a noncomputable real number has no such algorithm.
Almost every real number is noncomputable because there are only countably many algorithms.
Noncomputable Number
See also
Computable Number, Noncomputable Function, Turing MachineExplore with Wolfram|Alpha
References
Turing, A. M. "On Computable Numbers, with an Application to the Entscheidungsproblem." Proc. London Math. Soc. Ser. 2 42, 230-265, 1937.Cite this as:
Weisstein, Eric W. "Noncomputable Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NoncomputableNumber.html