Re: Replacement of Cardinality

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.

... 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.