Why not allow other symbols from some more complicated numbering system or alphabet? In fact, none of these changes makes the slightest difference to what can be in principle achieved, though some make a certain amount of difference to the economy of the operations (as would certainly be the case if we allowed more than one tape). The class of operations performed, and thus come under the heading of ‘algorithms’ (or ‘computations’ or ‘effective procedures’ or ‘recursive operations’), would be precisely the same as before even if we broadened the definition of our machines in all these ways at
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