Re: Replacement of Cardinality

On 8/19/2024 1:20 PM, Chris M. Thomasson wrote:

On 8/19/2024 10:17 AM, Moebius wrote:

Am 19.08.2024 um 18:58 schrieb Jim Burns:
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You got it totally wrong!
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The dark unit fractions are smaller than the (all) visible ones.
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Now: The visible unit fraction don't have a smallest one (of course), but the dark unit fraction do (at least in mückenmath)!
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WM: "Dark unit fractions have a smallest element."
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See?!
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WM: "Visible unit fractions have the [or rather *a*] lower bound 0."
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Right, but the dark unit fractions ARE BETWEEN 0 and all the visible unit fractions.
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See: https://en.wikipedia.org/wiki/Infinitesimal
and: https://en.wikipedia.org/wiki/Hyperreal_number
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WM: "No smaller [dark] unit fractions [than the smallest one] is existing, because no larger [dark] natnumber {than the largest one] is existing."
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Right!

 Is this one of WM's dark unit fractions:
 1 / (hyper_really_really_tiny_small)
 The funny part is that hyper_really_really_tiny_small should really be:
 hyper_really_really_large
 lol. What a joke.

In this sense... Forget about unit fractions, WM thinks that there is a largest natural number. This right there is radically ridiculous to me. Unit fractions aside for a moment...