Re: how (point at infinity)

On 06/15/2024 08:58 AM, Moebius wrote:

Am 14.06.2024 um 20:52 schrieb Jim Burns:

On 6/14/2024 12:39 PM, WM wrote:

>
Just seen here:
>
"number(s)" (WM) seems to refer to "natural number(s)" in this context.
>

WM (Proof by contradiction):
[Assume:] Every number has ℵo successors.

>
Actually, we do not have to assume that, since it can be proved (in the
context of mathematics/set theory).
>
An e IN: card({m e IN : m > n}) = ℵo.
>

If every number is subtracted the successors remain.

>
Huh?! Just a silly (psychotic) claim. If _every_ number "is subtracted"
(based on "the set of numbers+their successors"), then NO numbers (and
hence no successors) "remain" [in the new/resulting set]. (After all,
the successors of any number are numbers too.*)
>
What did WM prove here? That he's a complete idiot?
>
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*) An e IN: {m e IN : m > n} c IN.

If oo - oo = 0, or, N - N = 0 for a large number N,
vis-a-vis the notation IN for Natural zahlen, then
where one usually writes 0, 1, 2, ... for the numbers
then it's as well oo - 0, 1, 2, ... for the numbers,
about where there's a model of the naturals where
the naturals are compact and have a fixed-point at
infinity, for example about number theorists' "point
at infinity" or geometers' "point at infinity".
Usual number theorists about the compactification
of integer spaces and geometers about the projective
point at infinity, ..., if idiots, are on an idiot
scale, or, "Feldman is not an idiot, despite any
idiot scale".