Re: Cantor Diagonal Proof

On Fri, 4 Apr 2025 17:02:57 +0100, Mike Terry wrote:

On 04/04/2025 05:22, Lawrence D'Oliveiro wrote:

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On Fri, 4 Apr 2025 04:15:39 +0100, Mike Terry wrote:
 

On 04/04/2025 03:29, Lawrence D'Oliveiro wrote:

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On Fri, 4 Apr 2025 02:41:09 +0100, Mike Terry wrote:
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On 03/04/2025 23:18, Lawrence D'Oliveiro wrote:
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The definition of a “computable number” is that for any integer N,
there is an algorithm that will compute digit N of the number in a
finite sequence of steps.
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Does the Cantor diagonal construction fit this definition? Yes it
does.
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No it doesn't, because for a computable number the algorithm cannot
have an infinite amount of input data.

 
It doesn’t need to. To compute the Nth digit of the diagonal, it only
needs N * (N + 1) / 2 digits of the numbers in the first N entries of
the table.
 

Yes it does.  The missing number has infinitely many digits ...

Any given one of which can be computed in a finite time, with a finite
amount of data. That’s the definition of “computable”.