Based on the logic of what was in the machine, Turing showed that any computable function could be calculated," Kahn said.

Mathematicians had been thinking about computable functions for some time.

Recall that a

computable function must be specifiable by a finite number of bits.

This is the well known principle that for any

computable function, there exist distinct multiple programs that will compute it.

The function F is a

computable function that is continuous in its (d + 2) arguments however it is also analytic in the variable [theta].

2] is computable function, defined for all x [member of] [[SIGMA].

2] is a computable function, defined for all x [member of] [[SIGMA].

Computable functions may or may not be combinatorial, and vice-versa.

All of the models of effective computability that have been proposed to date have given rise to the same class of effectively

computable functions.