Re: Cantor Diagonal Proof

On 15/04/2025 05:42, Lawrence D'Oliveiro wrote:

Here’s my counterexample list: write out the whole numbers
(non-negative integers) from 0 in increasing order, and flip the
digits of each one so that the digit from the 10⁰ place goes to the
10¯¹ place, 10¹ to 10¯² etc:
      0.0000000000000...

0.1

     0.1000000000000...

0.11

     0.2000000000000...

0.111

     0.3000000000000...

0.1111

     ...

You'll have to be more specific.

     0.9000000000000...

0.11111

     0.0100000000000...

0.111111

     0.1100000000000...

0.1111111

     0.2100000000000...

0.11111111

     0.3100000000000...

0.111111111

     ...

If you're allowed to skip, so is Cantor.

     0.9100000000000...

0.1111111111

     0.0200000000000...

0.11111111111

     ...

0.11111111111...

 Notice an interesting property of the list:

Yes. It's missing 1/9. Oops.

So even in a list which we already know does not contain every
possible real number, the Cantor construction fails to find one of the
missing ones.

For the re-match you'd better add 1/9 by hand.
Cantor 1 D'Oliveiro 0.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
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