Re: Replacement of Cardinality

Jim Burns pretended :

On 8/8/2024 5:56 PM, FromTheRafters wrote:

Chris M. Thomasson has brought this to us :

On 8/8/2024 3:30 AM, FromTheRafters wrote:

on 8/8/2024, WM supposed :

Le 08/08/2024 à 00:17, Moebius a écrit :

>

Actually, his "thinking process" is simple:
"Since there is a gap (space) between adjacent unit fractions and all unit fractions are in the interval (0, 1], there must be FINITELY MANY of them (i.e. a first/smallest one)."

>
No, that is nonsense. There are not finitely many unit fractions.

>
Then stop assuming that there is a first and last element.

>
The first unit fraction is 1/1, there is no last one...

>
... or there is a last one but no first one.

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... or
(here is the "infinite" difference:)
each linear order has SOME SUBSET which is
without a first or without a last.
>
My opinion is that WM's idea of 'finite' omits
the 'subset' part of that,
and he thinks that
a set ordered with two ends is
more complete than
the same set with one or zero ends.
>
So, we say 'finite' and 'infinite' meaning one thing
and WM says 'finite' and 'infinite' meaning another.
And then we're off to the races.

Yes, and he adds a third so he has finite, potentially infinite, and infinite. Whenever someone makes a point in the infinite sense he says that it is only true for potentially infinite cases.