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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
Date: Thu, 14 Nov 2024 23:55:31 +0100
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Am 14.11.2024 um 23:48 schrieb Moebius:
> Am 14.11.2024 um 23:27 schrieb Chris M. Thomasson:
>> On 11/14/2024 2:19 PM, Moebius wrote:
>>> Am 14.11.2024 um 23:09 schrieb Chris M. Thomasson:
>>>> On 11/13/2024 3:28 PM, Moebius wrote:
>>>>> Am 14.11.2024 um 00:27 schrieb Moebius:
>>>>>> Am 13.11.2024 um 03:44 schrieb Chris M. Thomasson:
>>>>>>
>>>>>>> [...] different ways to represent zero?
>>>>>>>
>>>>>>> 0 = 3-4+1 = 4-4 = 2*0 = 0
>>>>>>>
>>>>>>> ect.
>>>>>>
>>>>>> Right. "3-4+1", "4-4", "2*0", "0", are just different NAMEs (math: 
>>>>>> TERMs) to denote (refer to) _one and the same_ number, namely zero 
>>>>>> (usualy, denoted with "0").
>>>>>>
>>>>>> Hint: Superman is Clark Kent.
>>>>>
>>>>> Superman = Clark Kent
>>>>>
>>>>
>>>> Superman = Clark Kent = Kal-El
>>>
>>> Right. The names "Superman", "Clark Kent" and "Kal-El" denote one and 
>>> the same person (being).
>>>
>>> We might extend that list by, say, "the only child of Jor-El and Lara 
>>> Lor-Van", etc.
>>>
>>> 0 = the predecessor of 1 = 1 - 1 = (the x in IR such that 1 + x = 1).
>>>
>>
>> For fun, define the "+" symbol to mean "having a child", so:
>>
>> (Jor-El + Lara Lor-Van) = (Superman = Clark Kent = Kal-El)
>>
>> ? lol.
> 
> Nope, that won't work.
> 
> For this we might define + , say, the following way:
> 
>        x + y = the child of x and y    if x and y have exactly one child
> 
>              = the set of the children of x and y     otherwise.
> 
> Then
> 
>        Jor-El + Lara Lor-Van = Superman = Clark Kent = Kal-El
> 
> and, say,
> 
>        Superman + Donald Trump = {} .
> 
> "having a child (or children)" is a predicate, while "the child of ... 
> and ..." is a term.

Actually, it would be even better to define + the following way:

          x + y = _the set_ of children of x and y    (where x,y are 
persons)

Then

         Jor-El + Lara Lor-Van = {Superman} = {Clark Kent} = {Kal-El} ,

         Adam + Eva = {Kain, Abel, ...}
and
         Superman + Donald Trump = {} .

Simpler and more consistent.