Re: More complex numbers than reals?

Am 11.07.2024 um 12:34 schrieb FromTheRafters:

Ben Bacarisse was thinking very hard :

Moebius <invalid@example.invalid> writes:
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Am 11.07.2024 um 02:28 schrieb Chris M. Thomasson:

On 7/10/2024 5:24 PM, Moebius wrote:

Am 11.07.2024 um 02:16 schrieb Chris M. Thomasson:
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{a, b, c} vs { 3, 4, 5 }
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Both have the same number of elements, [...]

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HOW do you know that? Please define (for any sets A, B):
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     A and B /have the same number of elements/ iff ___________________ .
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(i.e. fill out the blanks). :-)
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Hint: That's what Ben Bacarisse is asking for.
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Sure, it's "obvious" for us. But how would you define "have the same
number of elements" (in mathematical terms) such that it can be DEDUCED
(!) für certain sets A and B?
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________________________________________
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Ok, I'm slighty vicious now... :-)
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If a = b = c, {a, b, c} still has "the same number of elements" as {3,
4, 5 }? :-P

I see {a, b, c} and {3, 4, 5} and think three elements.

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Even if a = b = c?
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C'mon man! :-P

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Please, that's a red herring, and you know it!  No where did I say that
a, b and c stood for anything (i.e. that they might be variables in the
maths sense).  I this sort of context they are just distinct symbols.

 Indeed!

Nonsense. (See below.)

I sometimes try to steer WM away from 'math' symbols in sets like asking for a bijection of something like {elephant, rhinoceros, dune buggy} and {circle, square, megaphone}.

Here you used well estabished /names/ (constants) for certain objects which - as is well known - are not identical. With other words,
elephant =/= rhinoceros
elephant =/= dune buggy
rhinoceros =/= dune buggy,
etc.
Just using DIFFERENT (but arbitrary) symbols, say "a", "b", "c", does not ensure for that (i.e. a =/= b, a =/= c, b =/= c).
Actually, even a = b = c is POSSIBLE in this case. (Leading to card({a, b, c}) = 1.)
Now consider the two (different) names ("symbols") "turtle", "chelonian".
Does {turtle, chelonian} contain 2 elements, huh?!