Re: how (point at infinity)

On 06/15/2024 09:35 AM, Moebius wrote:

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:

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Just seen here:
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"number(s)" (WM) seems to refer to "natural number(s)" in this context.
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WM (Proof by contradiction):
[Assume:] Every number has ℵo successors.

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

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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.*)
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What did WM prove here? That he's a complete idiot?
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_____________________________________________
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*) An e IN: {m e IN : m > n} c IN.

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If oo - oo = 0, or,

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

Sometimes instead of "undefined" we say "indeterminate form".
Sometimes "indeterminate forms", are, "defined".
If WM is an idiot, why are you talking to him?
Then, my dear Moebius, or Meebius if you will,
the point is that WM is a poor example of
what is an example of contradictory notions
after the confounding of their conflation,
with each other, illustrating a number of
what are exercises in the avoidance and then
especially what should be the resolution or
abeyance of the, "inductive impasse", where
arguments via induction are provided that
lead to halts, breaks, or fails.
Then, the "analytical bridges", or Analytische
Brucken, are these ideas about how after a
confounding that there's established a space
where inductive arguments that point toward
each other, never complete, indicate a meeting,
a meeting in the middle, "middle of nowhere",
that according to deductive inference,
they must cross.
Singularity theory, here mostly about the
most classical example being "division by zero",
and as to whether, where, and when that 0/0,
oo/oo, and so on are "indeterminate forms",
is: Multiplicity Theory.
I.e., singularities in closed theories,
are multiplicities in more open theories.