Re: More complex numbers than reals?

Ben Bacarisse was thinking very hard :

Moebius <invalid@example.invalid> writes:
>

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:
 

{a, b, c} vs { 3, 4, 5 }
 Both have the same number of elements, [...]

 HOW do you know that? Please define (for any sets A, B):
      A and B /have the same number of elements/ iff ___________________ .
 (i.e. fill out the blanks). :-)
 Hint: That's what Ben Bacarisse is asking for.
 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?
 ________________________________________
 Ok, I'm slighty vicious now... :-)
 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.

 Even if a = b = c = 1?
 C'mon man! :-P

>
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! 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}. Bijections work for any sets, not just numerical ones -- easier to demonstrate with numbers though because you can use set builder notation instead of just roster form for really large 'number cumbersome' sets.