On 5/4/2025 2:21 PM, Richard Heathfield wrote:Quoth Alan Turing:On 04/05/2025 18:55, olcott wrote:IT IS NOT COMPUTING FUNCTION THENChanging my words then rebutting these changed>
words is dishonest.
>
Functions computed by Turing Machines require INPUTS
and produce OUTPUTS DERIVED FROM THESE INPUTS.
Counter-example: a Turing Machine can calculate pi without any input whatsoever.
>
As Mikko rightly said: a Turing machine does not need to require an input.
>
(viii) The limit of a computably convergent sequence is computable.
From (viii) and TT— 4(1—i-|--i—...) we deduce that TT is computable.
No input required.
IT IS NOT COMPUTING FUNCTION THENThat's a very second-rate summary of computability. Turing was far more interested in whether a computation was possible than whether it needed inputs. Do most computations need inputs? Most useful ones that we care about, sure. But all? By no means.
IT IS NOT COMPUTING FUNCTION THEN
IT IS NOT COMPUTING FUNCTION THEN
Computable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion of algorithms, in the sense that a function is computable if there exists an algorithm that can do the job of the function, i.e. given an input of the function domain it can return the corresponding output.
https://en.wikipedia.org/wiki/Computable_function
*Computer science is ONLY concerned with computable functions*Computer science is concerned with the Halting Problem.
The Halting Problem is concerned with an incomputable function.
Therefore computer science is concerned with at least one incomputable function.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
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