A number which can be computed to any number of digits desired by a Turing machine. Surprisingly, most irrationals are not computable numbers!
Computable Number
See also
Chaitin's Constant, Closed-Form SolutionExplore with Wolfram|Alpha
References
Penrose, R. The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford, England: Oxford University Press, 1989.Trott, M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, p. 105, 2004. http://www.mathematicaguidebooks.org/.Turing, A. M. "On Computable Numbers with an Application to the Entscheidungsproblem." Proc. London Math. Soc. 42, 230-265, 1936.Weihrauch, W. Computable Analysis. Berlin: Springer-Verlag, 2000.Wolfram, S. "Notes: Exact Solutions." A New Kind of Science. Champaign, IL: Wolfram Media, 2002.Referenced on Wolfram|Alpha
Computable NumberCite this as:
Weisstein, Eric W. "Computable Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ComputableNumber.html