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From: Moebius <invalid@example.invalid>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Mon, 19 Aug 2024 19:17:34 +0200
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Am 19.08.2024 um 18:58 schrieb Jim Burns:

You got it totally wrong!

The dark unit fractions are smaller than the (all) visible ones.

Now: The visible unit fraction don't have a smallest one (of course), 
but the dark unit fraction do (at least in mückenmath)!

WM: "Dark unit fractions have a smallest element."

See?!

WM: "Visible unit fractions have the [or rather *a*] lower bound 0."

Right, but the dark unit fractions ARE BETWEEN 0 and all the visible 
unit fractions.

See: https://en.wikipedia.org/wiki/Infinitesimal
and: https://en.wikipedia.org/wiki/Hyperreal_number

WM: "No smaller [dark] unit fractions [than the smallest one] is 
existing, because no larger [dark] natnumber {than the largest one] is 
existing."

Right!