Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: =?UTF-8?B?QW5kcsOpIEcuIElzYWFr?= Newsgroups: comp.theory Subject: Re: Correcting the definition of the halting problem --- Computable functions Date: Mon, 24 Mar 2025 19:46:38 -0600 Organization: Christians and Atheists United Against Creeping Agnosticism Lines: 70 Message-ID: References: <30c2beae6c191f2502e93972a69c85ff227bfd03@i2pn2.org> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Tue, 25 Mar 2025 02:46:39 +0100 (CET) Injection-Info: dont-email.me; posting-host="c28cbb8b97d3e83ccc5d9c5cd1c367aa"; logging-data="2268482"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/0IfoDfdS/x25PN+cVqa2W" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:XFK/2Fwx175BZ5gWG4VWzbEYmU0= Content-Language: en-US In-Reply-To: Bytes: 4444 On 2025-03-24 19:33, olcott wrote: > On 3/24/2025 7:00 PM, André G. Isaak wrote: >> In the post you were responding to I pointed out that computable >> functions are mathematical objects. > > https://en.wikipedia.org/wiki/Computable_function > > Computable functions implemented using models of computation > would seem to be more concrete than pure math functions. Those are called computations or algorithms, not computable functions. The halting problems asks whether there *is* an algorithm which can compute the halting function, but the halting function itself is a purely mathematical object which exists prior to, and independent of, any such algorithm (if one existed). > For example pure math functions don't have any specific > storage like a tape or machine registers. No they don't. Why would they? A mathematical function is simply a static mapping from elements of a domain to elements of a codomain. > This also would seem to mean that they would require > some actual input. > > >> The above copypasta doesn't address this. >> >> I pointed out that the domain of a computable function needn't be a >> string. The above copypasta doesn't address this. >> > > When implemented using an actual model of computation > some concrete form or input seems required. > >> I pointed out that there is no bijection natural numbers and strings, > > finite strings of decimal digits: [0123456789] > >> but rather a one-to-many relation. The above copypasta doesn't address >> this. > > "12579" would seem to have a bijective mapping to > a single natural number. The natural number 12579 maps equally to the (decimal) string '012579', '0012579',... so there is no bijection. >> >> I pointed out that the exact same sort of one-to-many relation exists >> between computations and strings. The above copypasta doesn't address >> this. >> > > I pointed out above that the finite string of x86 > machine code correctly emulated by EEE DOES > NOT MAP TO THE BEHAVIOR OF ITS DIRECT EXECUTION. But I was not talking about EEE. I was talking about the halting function. All you seem to be claiming above is that whatever EEE computes, it isn't the halting function. Everyone already agrees to that. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.