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

On 9/23/2024 8:56 AM, WM wrote:

On 23.09.2024 00:53, Richard Damon wrote:

Count down from infinity please,
what is the actual first number you use,
(not w-1, that isn't a number).
>
The problem is it doesn't exist,
because the numbers don't have a bound
on that end.

>
The problem is not non-existence.

Some things which we can describe
would require gibberish, impossibilities
if they existed.
Because we do not,
we _can not_ use gibberish,
we conclude that
gibberish.requirers do not exist.
You (WM) can declare that gibberish.requirers exist
until you're blue in the face;
gibberish.requirers will persist in
requiring gibberish.
We _can't_ accept gibberish.
There is _nothing there to accept_

Proof:
Chosse the greates existing number m.

Consider Boolos's ST
⎛ ∃{}
⎜ ∀x∀y∃z=x∪{y}
⎝ {set}.extensionality
∀m∃z=m∪{m}
¬∃m¬∃z=m∪{m}
Along with the claim  ∃m¬∃z=m∪{m}
that a greatest number exists
we have
¬∃m¬∃z=m∪{m}  ∧  ∃m¬∃z=m∪{m}
which is gibberish.

Then double it to get 2m.

Which is gibberish in the context of
m being the largest number.

Why didn't you choose 2m originally?

Because largest.number m is gibberish.

Obviously it exists.

largest m and m+1 2m and mᵐ
are all gibberish.
Talking about them
as though they make sense
does not change gibberish into sense.