Re: Incompleteness of Cantor's enumeration of the rational numbers

On 11/12/2024 6:05 AM, WM wrote:

On 11.11.2024 22:42, Chris M. Thomasson wrote:

On 11/11/2024 1:00 AM, WM wrote:

 

I(n) = [n - 1/10, n + 1/10]
can be translated until all rational numbers
1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, 2/4, 3/3, 4/2, 5/1, 1/6, 2/5, 3/4, 4/3, 5/2, 6/1,  ...
are midpoints.
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Obviously that is impossible because the density 1/5 of the intervals can never increase. It is possible however to shift an arbitrarily large (a potentially infinite) number of intervals to rational midpoints.

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I don't think you know how to take any natural number and turn it into a unique pair, and then back again via Cantor pairing.

 I don't think that you understand what's going on here.
 Regards, WM

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Why don't you show me your impl of Cantor Pairing. Take any natural and map it to a _unique_ pair. Then, map the unique pair back into the original natural number. It's not that hard. But I don't think you know how to do it.