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On 3/13/2024 11:58 PM, immibis wrote:You still did not explain what you mean by a mapping from D(D) to Halts(D,D). You only explained what you mean by Halts(D,D).On 14/03/24 05:31, olcott wrote:Halts(D,D) is a standard hypothetical function used to denote the the halting behavior that D(D) actually has. It is a notational convention.On 3/13/2024 11:22 PM, immibis wrote:>On 14/03/24 04:19, olcott wrote:>I did not say that precisely enough.>
There is no mapping from the specific TM/input pair:
H(D,D) to Halts(D,D)
Be even more precise because this doesn't seem to mean anything.
*The same question exists in a hierarchy of generality to specificity*
There is a mapping from D(D) to Halts(D,D).
There is a mapping from H1(D,D) to Halts(D,D)
There is no mapping from H(D,D) to Halts(D,D)
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What is a mapping from D(D) to Halts(D,D)? What do those words mean?
mapping from D(D) to Halts(D,D)
maps the actual behavior of D(D) to its actual halt status.
mapping from H1(D,D) to Halts(D,D)==1 meaning that D(D) halts.
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