Re: Replacement of Cardinality

On 8/31/2024 8:27 PM, Moebius wrote:

Am 01.09.2024 um 04:54 schrieb Chris M. Thomasson:
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I still don't know how WM is going to count the opposite way wrt:
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1/1, 1/2, 1/3, 1/4, ...
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That would be:
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..., 1/4, 1/3, 1/2, 1/1
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He can't do it.

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Yeah, but a function can do it.
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NUF(x) := the cardinal number of unit fractions that are smaller than x   (where x is a real number)
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Then we get, say, NUF(0) = 0 and, say, NUF(1/1) = aleph_0, NUF(1/2) = aleph_0, NUF(1/3) = aleph_0, etc.
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In general, for all x e IR, x > 0: NUF(x) = aleph_0.
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How does that fit with WM who thinks there is a smallest unit fraction to start counting from?