Re: Incompleteness of Cantor's enumeration of the rational numbers

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:
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[...] different ways to represent zero?
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0 = 3-4+1 = 4-4 = 2*0 = 0
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ect.

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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").
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Hint: Superman is Clark Kent.

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Superman = Clark Kent
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Superman = Clark Kent = Kal-El

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Right. The names "Superman", "Clark Kent" and "Kal-El" denote one and the same person (being).
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We might extend that list by, say, "the only child of Jor-El and Lara Lor-Van", etc.
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0 = the predecessor of 1 = 1 - 1 = (the x in IR such that 1 + x = 1).
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For fun, define the "+" symbol to mean "having a child", so:
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(Jor-El + Lara Lor-Van) = (Superman = Clark Kent = Kal-El)
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? 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.