Re: Turing computable functions

Am Tue, 25 Mar 2025 14:24:07 -0500 schrieb olcott:

Cannot possibly derive any outputs not computed from their inputs.

In particular, your HHH does not compute the behaviour of its input.

A Turing machine halt decider cannot possibly report on the behavior of
any directly executing process.
No Turing machine can every do this. This has always been beyond what
any Turing machine can ever do.
The best that any Turing machine halt decider can possibly do is
determine the behavior that an input finite string specifies.

Which iiis... surprise, whatever happens when you run it. You are
basically saying that simulators can make shit up.

When an input finite string specifies a pathological relationship with
its simulating halt decider the actual behavior that pathological
relationship derives must be reported because THAT IS THE BEHAVIOR THAT
IS SPECIFIED BY THIS INPUT FINITE STRING.

The relationship doesn't derive anything.
It is a tautology that a simulator reports what it reports. That doesn't
make that correct.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.