On 7/3/2026 9:19 PM, dbush wrote:Nope. Requirements are requirements for a reason. If they can't be satisfied, then that's just the way it is.On 7/3/2026 10:05 PM, olcott wrote:Impossible requirements are incorrect requirements.On 7/3/2026 8:58 PM, dbush wrote:>On 7/3/2026 9:52 PM, olcott wrote:>On 7/3/2026 5:51 PM, André G. Isaak wrote:The mathematical halting function:On 2026-07-03 16:37, olcott wrote:>On 7/3/2026 1:47 PM, André G. Isaak wrote:>On 2026-07-03 12:36, olcott wrote:>On 7/3/2026 1:18 PM, dbush wrote:>>If an algorithm takes an input and produces an output, that is by definition a mapping.That only proves that the definition is incoherent.
The coherent way that it actually works is that
inputs are transformed into outputs by applying
finite string transformation rules to inputs to
derive outputs.
Apparently you don't understand the difference between a mapping and an algorithm. They are two different things.
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André
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A function that ignores its input and only returns 0
is not any sort of halt function.
He was defining 'mapping', not 'halt function'.
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André
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A actual halt function must compute
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When you actually implement this concretely
We find that it is not possible, as Linz and others have proved.
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I would like to have a single algorithm that can tell me whether any arbitrary algorithm with a given input will halt when executed directly, but unfortunately no such algorithm exists.
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