Re: Replacement of Cardinality

On 9/3/2024 7:55 PM, Richard Damon wrote:

On 9/3/24 7:31 AM, WM wrote:

On 02.09.2024 19:13, Richard Damon wrote:

On 9/2/24 12:56 PM, WM wrote:

On 01.09.2024 21:09, Chris M. Thomasson wrote:

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

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In general, for all x e IR, x > 0: NUF(x) = aleph_0.

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Don't get confused by that nonsense. Everybody knows that unit fractions are different from each other. Therefore they cannot be counted at the same x, let alone at less than all positive x, i.e., at zero.

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How does that fit with WM who thinks there is a smallest unit fraction to start counting from?

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I do not think that but I prove that by the simple fact that not more than one unit fraction can be lessequal than all unit fractions.
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Except that it starts with the incorrect assumption that such a unit fraction exists.

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No, it shows that no unit fractions exist unless a first one exists.
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Regards, WM

 But 1/1 is the FIRST unit fraction.
 You just can't count from the other end (that doesn't HAVE an end)

Yeah. Agreed. He is a big time finite type of person... Those three dots (...) make his brain want to bleed? ;^)