Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

On 10/11/2024 7:06 AM, Richard Damon wrote:

On 10/10/24 11:19 PM, Chris M. Thomasson wrote:

On 10/10/2024 6:38 PM, Richard Damon wrote:

On 10/10/24 2:32 PM, WM wrote:

If not all do exist,
te doubling yields larger natnumbers,
some of which have not existed before.
But that means potential infinity.

>
But there aren't any natural numbers that
have not existed before. That is just showing that
your "actual infinity" is a finite set that you grabbed on the way to infinity,
but didn't get there yet.

>

Actual infinity means
you need to wait until you get there.
The problem is
finite creatures can't do that,
so can't handle actual infinity.

What do you mean?
I can say all the natural numbers.
That was pretty fast for all of them. ;^)

>
Which names the set,
but not actually list the contents of that set.

Is a set
without a finite list  but
with a finite description
potential or actual?
It looks to me as though the consensus is:
we don't care what the answer is.
We have a description of ℕ and its elements,
free of mentions of 'potential' and 'actual'.
 From its description,
we can reason about it and its elements.
"Potential ℕ" vs. "actual ℕ" leaves unchanged
which claims we reason to.
I see them as in the same vein as
weekday.mathematics and Sunday.mathematics.[1]
A distinction without a difference.
And I see that indifference as there _by design_
It is why unwelcome mathematical results are accepted
not because mathematicians are paragons of rectitude
(no offense)
but because there is no weasel.ability in mathematics.
⎛ Not everyone appreciates that lack of weasel.ability.
⎝ Those who don't self.select to be non.mathematicians.
[1]
⎛
⎜ Most writers on the subject seem to agree that
⎜ the typical “working mathematician” is
⎜ a Platonist on weekdays and a formalist on Sundays.
⎜ That is, when he is doing mathematics,
⎜ he is convinced that
⎜ he is dealing with an objective reality
⎜ whose properties he is attempting to determine.
⎜ But then, when challenged to give
⎜ a philosophical account of this reality,
⎜ he finds it easiest to pretend that
⎜ he does not believe in it after all.
⎝
https://core.ac.uk/download/pdf/82047627.pdf
Some Proposals for Reviving the Philosophy of Mathematics
REUBEN HERSH
Department of Mathematics, University of New Mexico,
Albuquerque, New Mexico 87131