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The Turing Machine concept defines what is meant mathematically by an algorithmic procedure. Stated another way, a
function 
is effectively Computable Iff it can be computed by a
Turing Machine.
See also Algorithm, Computable Function, Turing Machine
References
Penrose, R. The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics.
Oxford, England: Oxford University Press, pp. 47-49, 1989.