Re: Hypothetical possibilities -- I reread this again more carefully

Am Sun, 21 Jul 2024 09:34:57 -0500 schrieb olcott:

On 7/21/2024 9:24 AM, joes wrote:

Am Sun, 21 Jul 2024 08:08:53 -0500 schrieb olcott:

On 7/21/2024 6:37 AM, Richard Damon wrote:

On 7/21/24 12:15 AM, olcott wrote:

(b) We know that a decider is not allowed to report on the behavior
computation that itself is contained within. Deciders only take finite
string inputs. They do not take executing processes as inputs. Thus
HHH is not allowed to report on the behavior of this int main() {
DDD(); }.

That IS exactly the input.

The behavior of emulated DDD after it has been aborted changes the
behavior of the directly existed DDD.

A deterministic program can't change. It was always going to be aborted.

When the second call of what would otherwise be infinite recursion is
required to be aborted to prevent the infinite execution of the first
call this proves that HHH(DDD)==0 is correct even though the directly
executed DDD() halts.

The second call stops simulating just like all others.

Therefore we map the finite string input to HHH(DDD) to the behavior
that it species on the basis of DDD correctly emulated by any pure
function HHH that can possibly exist.

The basis is the direct behaviour.

Unless you think the idea of UTMs is wrong-headed nonsense the behavior
of DDD correctly emulated by HHH determines the actual behavior
specified by the input to HHH(DDD).

HHH is not an UTM.

--
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.