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Re: UTM Theorem vs the identity function

From pa@see.signature.invalid (Pierre Asselin)
Newsgroups comp.theory
Subject Re: UTM Theorem vs the identity function
Date 2025-10-21 18:50 +0000
Organization PANIX Public Access Internet and UNIX, NYC
Message-ID <10d8km3$ndh$1@reader2.panix.com> (permalink)
References <10d8cp6$26v9$1@dont-email.me>

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Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> wrote:

> If the UTM Theorem states there's a u such that u(e,x) = f(x) where both
> are defined and both are undefined when either is undefined, is that
> interesting or surprising to anybody?

Replace "there's a u" by "there is a u such that for all f there is an e"

> The identity function is valid for u and forces that e = f. Job done.

  * u is a computable function;
  * f is a computable function;
  * e is the Gödel number of a Turing machine that computes f.
How can e and f be equal ?

-- 
pa at panix dot com

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UTM Theorem vs the identity function Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-21 17:35 +0100
  Re: UTM Theorem vs the identity function pa@see.signature.invalid (Pierre Asselin) - 2025-10-21 18:50 +0000
    Re: UTM Theorem vs the identity function Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-22 03:48 +0100
      Re: UTM Theorem vs the identity function olcott <polcott333@gmail.com> - 2025-10-21 21:51 -0500
        Re: UTM Theorem vs the identity function Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-22 04:02 +0100
          Re: UTM Theorem vs the identity function --- Gödel olcott <polcott333@gmail.com> - 2025-10-21 22:35 -0500
      Re: UTM Theorem vs the identity function pa@see.signature.invalid (Pierre Asselin) - 2025-10-22 18:45 +0000
        Re: UTM Theorem vs the identity function Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-23 03:34 +0100
          Re: UTM Theorem vs the identity function pa@see.signature.invalid (Pierre Asselin) - 2025-10-23 18:50 +0000
  Re: UTM Theorem vs the identity function Mikko <mikko.levanto@iki.fi> - 2025-10-22 12:39 +0300
    Re: UTM Theorem vs the identity function Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-22 12:05 +0100
      Re: UTM Theorem vs the identity function Mikko <mikko.levanto@iki.fi> - 2025-10-23 11:12 +0300

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