Quote:
Originally Posted by Kriminal99
A halting machine attempting to operate upon itself would cease it's normal function and simply always loop.
A function which gives 0 if the input function is defined would cease it's normal function and always loop if operated upon itself.
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The Halting Problem requires *both* the function and a *finite* input. If as you suggest, you do an infinite regress of feeding the halting algorithm itself with the input to the algorithm itself, with the input to the algorithm itself, with the input to the algorithm itself,
ad nauseum, then you've really only proved the theorem correct!
The Halting Problem theorem is only saying that a *general* algorithm cannot be developed that works for *all* function/finite-input pairs. You could feed the algorithm to itself with a *different* finite input, and it would halt. The fact that the infinite regress case does not work simply proves the theorem.
So,
Quote:
Originally Posted by Kriminal99
Every Halting problem undecidability proof asks us to assume that such functions could operate on themselves.
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is not at all an "assumption" its the fact that proves the theorem....
People seldom see the halting and painful steps by which the most insignificant success is achieved,
Buffy
