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

On 10/20/2024 06:36 AM, Jim Burns wrote:

On 10/19/2024 9:56 PM, Ross Finlayson wrote:

On 10/19/2024 03:54 PM, Jim Burns wrote:

On 10/19/2024 2:19 PM, WM wrote:

On 19.10.2024 18:04, Jim Burns wrote:

>

The least.upper.bound of finites is ω

>
What ω is
is such that
k < ω  ⇔  k is a finite ordinal.
>
No k exists such that
k is a finite and k+1 > k is not a finite.
>
No k exists such that
k is an upper.bound of the finites.
>
ω is but anything prior to ω isn't
an upper.bound of the finites.
>
ω is the least.upper.bound of the finites.
>

The least.upper.bound of doubled finites is ω

>
A doubled finite is finite.
>
No k exists such that
2⋅k is a finite and 2⋅k+2 > 2⋅k is not a finite.
>
No k exists such that
2⋅k is an upper.bound of the doubled finites.
>
ω is but anything prior to ω isn't
an upper.bound of the doubled finites.
>
ω is the least.upper.bound of the doubled finites.

>
Isn't mathematics true?

>
It's impossible for there to be
  false mathematics.conclusions with
  true mathematics.hypotheses.
>
How do we know they're impossible?
>
Starting from [insert hypotheses],
what must.be.true conclusions are known of?
>
Why (exo.mathematically) choose
[insert hypotheses] to be hypotheses?
>

The omega is usually called
a fixed-point besides being
a limit ordinal, also it's called
a compactification
or one-point compactification of the integers
for the most usual sort of idea of
a non-standard countable model of integers
with exactly one infinite member.

>
Is there some sort of protocol
which you (RF) recognize
in order to talk about a thing
and not.talk about things not.that?
>
>

Here there's freedom of speech it one of
what we call constitutional liberties, and
it's sort of qualified under human rights
yet what it means is that no there's no
constraint to shut up and compute when
the wastecan's on fire.
It's not like we haven't exchanged thousands
and thousands of letters, which overall bear
at least a surprisingly passing resemblance to
civilized discourse, and already have much
discussion where it's established there are
more than the finite models of things, while
also all of them.
Then the "limit point" idea of omega, the
limit ordinal and fixed point, and also
"limit point", yes is intended to convey
that it's perceived a topology of the natural
integers where they're compact with the usual
idea of the one-point compactification which
some have as _already exists_ and then that
also there's a topology on these thusly and
that it's more about the "Integer Continuum"
this way.
So, it was deemed relevant, and the terms
_are_ in terms of each others' definitions,
so it's relevant and relevance logic, thus
I imagine that it's not simply a rejection
of fallacies of quasi-modal logic, then that
also it's part of the greater dialectic and
showing up that while sometimes it's easy to
brick-bat a troll, +how+ it's done is relevant
when others can later soft-ball straw-man that, also.
Good luck and warm regards, there's a great
multitude of infinitary theories and of only
particularly the regular, including the regular
in the extra-ordinary, and otherwise at least
three definitions of continuity, and, maybe
always lesser or greater than standard models
of integers.