Re: 2N=E

On 10/31/2024 4:17 AM, WM wrote:

On 31.10.2024 00:49, Jim Burns wrote:

There is no n.sequence between 0 and ω
without a n+n.sequence between 0 and ω.
>
'Infinite' does not mean what you want it to mean.

>
Then infinity means only

'Infinite' means 'not finite'.
A set is finite if countable.to from nothing,
  finite even if countable.to via dark.
ω is first after all countable.to ordinals.
If ω is countable.to,
then
ω+1 is countable.to and is not before ω
ω is not.countable.to.
If ω-1 is existing.and.countable.to
then
(ω-1)+1=ω is countable.to  and
(ω-1)+1+1=ω+1 is countable.to and not before ω
ω-1 is not existing.and.countable.to
If ω-1 is existing.and.not.countable.to
then
no countable.to are after ω or after ω-1  and
ω-1 is firster.than.ω after all countable.to.
ω-1 is not existing.and.not.countable.to
ω-1 is not existing.
ω is not.countable.to.

Then infinity means only
an interval on the real line that
can be extended by a factor 2
when _all_ its numbers
(including all n+n sequences)
are doubled.

Any finite
can be counted to, and
can be counted to twice, and
its double can be counted to and
its double is finite.
But what about the last finite?
The last finite is gibberish.
Anything countable.to is countable.past.
Anything countable.past is not.last.countable.

Hilbert, Cantor, and others
call that potential infinite.

Does it matter what it's called?
It is what it is.
A finite sequence of only
true.or.not.first.false 𝗰𝗹𝗮𝗶𝗺𝘀
holds a 𝗰𝗹𝗮𝗶𝗺 that,
after all swaps,
Bob is not in any visible or dark room
which he has ever been in.
We know that it is a true 𝗰𝗹𝗮𝗶𝗺
without our being Chuck Norris, by
examining those finitely.many 𝗰𝗹𝗮𝗶𝗺𝘀 and
seeing that they are each true.or.not.first.false.