Re: Cantor Diagonal Proof

On Mon, 7 Apr 2025 09:21:25 +0100, Richard Heathfield wrote:

On 07/04/2025 08:33, Lawrence D'Oliveiro wrote:
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On Sun, 6 Apr 2025 23:38:25 +0100, Richard Heathfield wrote:
 

On 06/04/2025 23:01, Lawrence D'Oliveiro wrote:
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On Sun, 6 Apr 2025 07:53:06 +0100, Richard Heathfield wrote:
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After infinitely many steps ...

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I.e. never.

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If you mean you can never know all the digits, hey, you're right.
No algorithm can derive the number. It's incomputable.

 
That’s not what “incomputable” means.

 
Yeah, it is. We've already had this argument. Turing won:  "The
"computable" numbers may be described briefly as the real numbers whose
expressions as a decimal are calculable by finite means."

You didn’t even read to the end of his first paragraph: “According to my
definition, a number is computable if its decimal can be written down by a
machine”.

Second paragraph: “The include, for instance, the real parts of all
algebraic numbers, the real parts of the zeros of the Bessel functions,
the numbers π, e, etc”.

Tell me your interpretation of how the digits of π “as a decimal are
calculable by finite means”.

Like anything in mathematics, if you're going to overturn a
long-established proof you're going to need a better argument than that
you don't understand what it proves.

Go on, then, show the flaw in my proof by induction. Because if proof-by-
induction is not a “long-established proof”, then tell me what is.