Re: Replacement of Cardinality

On 8/19/2024 2:12 PM, FromTheRafters wrote:

Chris M. Thomasson submitted this idea :

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!

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

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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...

 In order for there to be a smallest unit fraction n/d then d would have to be a largest natural number.

Exactly. Why does WM seem to be permanently stuck in finite ville, only to adventure out from time to time in the darkness of the forest?

For some reason (or none at all) he thinks it makes a difference to his argument to simply invert it.