We are not asking whether all digital computers would do well in the game nor whether the computers at present available would do well, but whether t… - Alan Turing

To each computable sequence there corresponds at least one description number, while to no description number does there correspond more than one computable sequence. The computable sequences and numbers are therefore enumerable.

A man provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal machine.

If an ɑ-machine prints two kinds of symbols, of which the first kind (called figures) consists entirely of 0 and 1 (the others being called symbols of the second kind), then the machine will be called a computing machine.