Re: how (point at infinity)

Am 15.06.2024 um 18:19 schrieb Ross Finlayson:

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,

oo - oo usually is undefined (see: https://en.wikipedia.org/wiki/Extended_real_number_line#Arithmetic_operations)
While on the other hand:
N - N = 0 for a large number N [=/= oo],
Right.
Is there anything you want do say, Ross?
Something which is RELATED to my post you quoted?