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A comment on How the Square Root of 2 Became a Number. Parent comment

Re:How the Square Root of 2 Became a Number by Edwinr95 on Friday June 21, 2024 @12:57PM (#40751441)
No, the statement holds perfectly fine for the rationals.
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Re:How the Square Root of 2 Became a Number by crdrost on Friday June 21, 2024 @01:34PM (#40751820)
The basis for this statement holds, but what the statement implies does not.

That is, the numbers are a subset of the rationals, but it does not follow that we can't describe a rational with a number. In fact the rationals between [0, 1) have a well known numbering,

    [ 0/1, 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5, 
      1/6, 5/6, 1/7, 2/7, 3/7, 4/7, 5/7, 6/7, 1/8, 3/8, ... ]
where one increments the denominator and then goes through all numerators but keeps only numerators which have GCD 1 with the denominator (since if they share a factor they were already listed).
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Re:How the Square Root of 2 Became a Number by LudwigNagasena on Friday June 21, 2024 @01:26PM (#40751744)
There is a 1-to-1 mapping between integers and rationals.
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