Re: Turing Machine computable functions MUST apply finite string transformations to inputs

On 4/30/2025 7:17 PM, André G. Isaak wrote:

You are still hopelessly confused about your terminology.
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Computable functions are a subset of mathematical functions, and mathematical functions are *not* the same thing as C functions. Functions do not apply "transformations". They are simply mappings, and a functions which maps every pair of natural numbers to 5 is a perfectly legitimate, albeit not very interesting, function.
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What makes this function a *computable function* is that fact that it is possible to construct a C function (or a Turing Machine, or some other type of algorithm) such as int foo(int x, int y) {return 5;} which computes that particular function; but the C function and the computable function it computes are entirely separate entities.

 computes the sum of two integers
by transforming the inputs into an output.
int sum(int x, int y) { return x + y; }
 Computes no function because it ignores its inputs.
int sum(int x, int y) { return 5; }