Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how

On 5/6/2024 4:28 PM, WM wrote:

Le 06/05/2024 à 22:16, Jim Burns a écrit :

On 5/6/2024 2:59 PM, WM wrote:

Le 05/05/2024 à 19:59, Jim Burns a écrit :

On 5/3/2024 4:31 PM, WM wrote:

If all could be counted to,
they would not remain after every counted number.

>
Of those which CAN be counted.to,
each CAN be counted to.

>
Of course.

Of those which CAN be counted.to,
each CAN be counted to,
and
none are after all which CAN be counted.to

But ∀n which can be counted to:
|ℕ \ {1, 2, 3, ..., n}| = ℵo.

All which canNOT be counted.to are not.in ℕ
ℕ\{1,2,3,...,n} holds ℵ₀.many countable.to numbers
and only countable.to numbers.
You (WM) appear to be treating as reliable
this step, which is not reliable:
| For each countable.to number,
| there are ℵ₀.many countable.to numbers,
| such that they follow it.
---------------------------------
☠ There are ℵ₀.many countable.to numbers
☠ such that, for each countable.to number,
☠ they follow it.
However, that is not reliable.

Nevertheless almost all, namely ℵo, remain.

>
Of those which CAN be counted.to,
each CAN be counted to,
and
none remain after all which CAN be counted.to

>
Count to one that has
less than ℵo numbers which
cannot be counted to.

"Infinite" does not mean "humongous"

Fail.

What does "infinite" mean?
Fail.