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

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?