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

On 09/08/2024 09:59 PM, Jim Burns wrote:

On 9/8/2024 6:34 PM, Ross Finlayson wrote:

On 09/08/2024 12:13 PM, Jim Burns wrote:

>

[...]

>
It's already been thoroughly elaborated and
as attached to formalistic symbolry,
that "Russell's thesis, of an antinomy" is that
the set of
the finite sets that don't contain themselves,
exactly like the ordinals are mostly simply modeled to be,
does and doesn't contain itself,

>
No.
The set of
the finite non.self.membered sets
is not itself a finite set.
Therefore, it is not in itself.
Secundum non datur.
>

blowing wide open that
there is a class of propositions
external [to] "tertium non datur".

>
It seems as though
you (RF) should re.evaluate
your reasoning here
in light of the set of
finite non.self.membered sets
not itself being a finite set.
>

Then,
"Russell's retro-thesis", is
  "forget I, Russell I, said that,
  and now that Frege's out of the way,
  think me and Whitehead made 1 + 1 = 2,
  after this brief 0 = 1 as it were",
asking you simply ignore his stated antinomy,
and furthermore your own conscience
as with regards to these matters.

>
1.
I wonder what your own conscientious response
will be to the infiniteness of the set of
all finite non.self.membered sets.
>
2.
It is an essential aspect of these discussions that
whatever is not being discussed
is not being discussed.
>
That essential aspect seems to be
what you (RF) consider
hypocritically ignoring
whatever is not being discussed.
>
Consider that it is possible for there to be
many discussions, with many different topics.
It is true at the same time
that
nonstandard analysis can be pursued
and
the complete ordered field doesn't hold
anything other than elements of
the complete ordered field.
>
>

Reading from Wertheimer, a sort of Gestalt
about points and space inversion:
https://www.youtube.com/watch?v=tODnCZvVtLg&t=1320s
"At times it seemed so clear that I need only write it down ...".
-- Max Wertheimer
As context expands there's nothing left out. The objects
of mathematics all live in one mathematical universe,
or "Hilbert's Infinite Living Working Museum of Mathematics",
as with regards to "Heraclitus' Hilbert's" and this and that,
where the Eleatics after the Ionians made for ideals what
advises the great fixtures from Greek to German idealism,
that here the linear continuum is particular in that all
models of the linear continuum coincide, vis-a-vis, their
inter-compatibility or "ponts", the bridges, as of after
the Integer Continuum the line-reals, the field-reals,
the signal-reals, of a Long-Line Continuum, a Linear Continuum,
all one thing.