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

On 10/25/2024 3:15 PM, WM wrote:

On 25.10.2024 21:05, Jim Burns wrote:

On 10/25/2024 12:57 PM, WM wrote:

A better question is:
why do you (WM) support it?

>
I support it in order to show that
your infinity is inconsistent.

>
My infinity? You mean
γ ∈ ⟦0,ω⦆  ⇔  ∀β ∈ ⦅0,γ⟧: ∃α: α+1=β
?

>
Mainly, among other points, the claim that
all unit fractions can be defined and he claim that
a Bob ca disappear in lossless exchanges.

The proof that all unit fractions can be defined
is to define them
as reciprocals of positive countable.to.from.0 numbers.
That describes all of them and only them.
More can be learned about all of them
by augmenting that description with
finitely.many only not.first.false claims,
which must be true.

Almost all unit fractions
cannot be discerned by definable real numbers.

>
All unit fractions are reciprocals of
positive countable.to.from.0 numbers.

>
That does not change the facts.

Clearly, the disagreement of proofs
does not change which claims you call facts.

If they are existing,
they are indiscernible, i.e. dark.

>
If it is existing,
it is a reciprocal of
a positive countable.to.from.0 number.

>
Most of them are indiscernible too.

𝗖𝗹𝗮𝗶𝗺𝘀 about the discernible.or.indiscernible
  which are in a finite sequence of 𝗰𝗹𝗮𝗶𝗺𝘀 such that
   each 𝗰𝗹𝗮𝗶𝗺 is not.first.false
must be true.

I haven't found a reason to discern.

>
Don't you claim that
every unit fraction can be discerned, i.e. separated from the smaller ones by a real number?

½⋅(⅟n+⅟(n+1)) existing is discerning?
I did not know that.
Here is some of what I 𝗰𝗹𝗮𝗶𝗺:
A finite sequence of only not.first.false 𝗰𝗹𝗮𝗶𝗺𝘀
  holds only true 𝗰𝗹𝗮𝗶𝗺𝘀.
A true 𝗰𝗹𝗮𝗶𝗺 is not.first.false.
𝗾 is not.first.false in ⟨𝗽 𝗽⇒𝗾 𝗾⟩
Ordinals 𝕆 are well.ordered and successored
Naturals ℕ are ordinals predecessored or 0
  such that all priors are predecessored or 0
Integers ℤ are differences of naturals
Rationals ℚ are quotients of integers (w/ non.0 denom)
Reals ℝ are points between splits of the rationals.