Re: Hypothetical possibilities V2

On 7/22/24 12:08 PM, olcott wrote:

void DDD()
{
   HHH(DDD);
   return;
}
 int main()
{
   HHH(DDD);
}
 Of the two hypothetical possible ways that HHH can be encoded:
(a) HHH(DDD) is encoded to abort its simulation.
(b) HHH(DDD) is encoded to never abort its simulation.
 We can know that (b) is wrong because this fails to meet the design requirement that HHH must itself halt.
 We also know that any simulation that must be aborted to prevent the infinite execution of the simulator is necessarily a non-halting input.
 

Remember, every HHH crreates a DIFFERENT "PROGRAM" DDD to decide on, and thus you don't have a case you can apply the property of the excluded middle.
In case (a) HHH(DDD) aborts and returns, so it returns to DDD and DDD Halts, so if HHH returned 0, it was wrong.
In case (b) HHH(DDD) never aborts, and as you admit, fails to be a decider.
We can show that for (a), that HHH was wrong by giving that same DDD (which still calls that HHH) to another emulator (like the (b) case) put in an unused location of memory, and it WILL emulate that input to the final state, thus proving you wrong.
This is what you HHH1 shows,