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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: More complex numbers than reals?
Date: Thu, 11 Jul 2024 15:17:54 +0200
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Am 11.07.2024 um 02:33 schrieb Chris M. Thomasson:
> On 7/10/2024 5:31 PM, Moebius wrote:
>> 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. 

Actually, it's not, since we don't know if a, b, c are "pairwise 
distinct" (see below). Sorry about that.


>>>> 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?
Yes?

>>>> ________________________________________
>>>>
>>>> Ok, I'm slighty wicked 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?
>>
>> C'mon man! :-P
> 
> Well, In my programming mind, { a, b, c } and { 3, 4, 5 } have the same 
> number of elements. Is this bad?

Yes it's bad. :-)

If a = b = c, then {a, b, c} only contains 1 element.

Don't mix up the symbols used for denoting some objects with the objects 
denoted by the symbols.

In this case there are 3 (different) symbols, namely "a", "b", "c", but 
it is not excluded that they all denote the same object, say, the number 
1. Then {a, b, c} = {1}.

I hope "In my programming mind" knows the difference beween using

       a, b, b

and

       "a", "b", "c".

:-)

Hint (Python):

a = 1

print(a)

print("a")

:-P