Re: Replacement of Cardinality

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:
>
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!

 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...

In order for there to be a smallest unit fraction n/d then d would have to be a largest natural number. For some reason (or none at all) he thinks it makes a difference to his argument to simply invert it.