A noncomputable function is a function for which no Turing machine computes the value on every input in its domain. For functions on the
nonnegative integers, this means that no algorithm halts with output 
for every allowed input 
. The characteristic function of an undecidable set is noncomputable.
Noncomputable Function
See also
Computable Function, Halting Problem, Noncomputable Number, UndecidableExplore 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 Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NoncomputableFunction.html