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Re: Cantor Diagonal Proof

From Julio Di Egidio <julio@diegidio.name>
Newsgroups sci.math
Subject Re: Cantor Diagonal Proof
Date 2025-10-22 16:19 +0200
Organization A noiseless patient Spider
Message-ID <10dap6b$f4ei$1@dont-email.me> (permalink)
References <vsn1fu$1p67k$1@dont-email.me> <10dajcd$j82n$1@dont-email.me>

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On 22/10/2025 14:40, Tristan Wibberley wrote:
> On 03/04/2025 23:18, Lawrence D'Oliveiro wrote:
>> The Cantor diagonal construction is an algorithm for computing an
>> incomputable number.
> 
> Doesn't it merely /define/ the number?

It does define the "number", 1) in such a way that it is a "number";
2) it also proves it cannot be in the list; whence 3) the list cannot
be complete.

Of course, to the detail of the formal construction, what kind of
"number" that exactly is matters, but the general form of the argument
is just that.

> here, every generated "new" number is eventually included in the list.

For *any* putative such list, a "number" can be constructed such that...

Hope that helps,

Julio

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Thread

Re: Cantor Diagonal Proof Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-22 13:40 +0100
  Re: Cantor Diagonal Proof Richard Heathfield <rjh@cpax.org.uk> - 2025-10-22 14:29 +0100
    Re: Cantor Diagonal Proof Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-22 16:02 +0100
      Re: Cantor Diagonal Proof Julio Di Egidio <julio@diegidio.name> - 2025-10-22 17:17 +0200
      Re: Cantor Diagonal Proof Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-22 17:26 +0100
    Re: Cantor Diagonal Proof WM <wolfgang.mueckenheim@tha.de> - 2025-10-23 16:51 +0200
  Re: Cantor Diagonal Proof Julio Di Egidio <julio@diegidio.name> - 2025-10-22 16:19 +0200
    Re: Cantor Diagonal Proof Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-22 17:32 +0100
    Re: Cantor Diagonal Proof WM <wolfgang.mueckenheim@tha.de> - 2025-10-23 16:56 +0200
      Re: Cantor Diagonal Proof: un-_Countable_ or un-_Cartesian_? Ross Finlayson <ross.a.finlayson@gmail.com> - 2025-10-23 12:27 -0700
  Re: Cantor Diagonal Proof "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-22 12:15 -0700
  Re: Cantor Diagonal Proof wm <wolfgang.mueckenheim@tha.de> - 2025-10-23 16:34 +0200
    Re: Cantor Diagonal Proof Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-23 20:43 +0100
      Re: Cantor Diagonal Proof WM <wolfgang.mueckenheim@tha.de> - 2025-10-24 22:35 +0200

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