Re: The non-existence of "dark numbers"

Liste des GroupesRevenir à s math 
Sujet : Re: The non-existence of "dark numbers"
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.math
Date : 27. Mar 2025, 23:58:35
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <b9c83a78-1304-499c-acc2-5e705e89dbf5@att.net>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
User-Agent : Mozilla Thunderbird
On 3/27/2025 4:23 PM, WM wrote:
Am 26.03.2025 um 22:09 schrieb Jim Burns:
On 3/26/2025 2:37 PM, WM wrote:

"WM-logic" says that
lossless exchanges at finite steps
are lossless
>
For a set larger than
any set such that
  emptier.by.one and smaller.by.one are the same,
emptier.by.one and smaller.by.one aren't the same.
>
Countable sets have only counted elements.
Sets of counted only have counted elements.
Sets of countable only have countable elements.

Lossless exchanges
like every other event
can happen only at a finitely indexed step.
But there
it is excluded by logic.
An exchange of same.sized sets is lossless.
  (∀A: ¬I(A) ⇒ A≠Y)  ⇒  I(Y)

⎜ A set Y different from
⎜  each set A without Property I
⎜ is
⎝ a set Y with Property I.
∀A: #A < #Aᣕᵃ  ⇒  #A ∈ {#C:#C<#Cᣕᶜ}

⎜ For each finite set,
⎝ its size is in the set of all finite sizes.
∀A: #A ∉ {#C:#C<#Cᣕᶜ}  ⇒  #A = #Aᣕᵃ

⎜ Each set with its size not.in
⎜ the set of all finite sizes
⎜ is not a finite set.
⎝  ¬(#A > #Aᣕᵃ)
∀#A ∈ {#C:#C<#Cᣕᶜ}:
#A = #{#C:#C<#A}  ∧  {#C:#C<#A} ⊆ {#C:#C<#Cᣕᶜ}

⎜ For each finite size, there is
⎝ a subset of that size   of all finite sizes.
∀#A ∈ {#C:#C<#Cᣕᶜ}:  #A < #Aᣕᵃ ∈ {#C:#C<#Cᣕᶜ}

⎜ For each finite size, there is
⎝ a finite size larger than it is.
∀#A ∈ {#C:#C<#Cᣕᶜ}:
#A < #{#C:#C<#Aᣕᵃ}  ∧  {#C:#C<#Aᣕᵃ} ⊆ {#C:#C<#Cᣕᶜ}

⎜ For each finite size, there is
⎝ a larger subset   of all finite sizes.
∀#A ∈ {#C:#C<#Cᣕᶜ}:  #A ≠ #{#C:#C<#Cᣕᶜ}

⎜ Each finite size isn't the size of
⎝ the set of all finite sizes.
#{#C:#C<#Cᣕᶜ} = #{#C:#C<#Cᣕᶜ}ᣕᴮᵒᵇ

⎜ The set of all finite sizes isn't smaller than
⎝ a fuller.by.one set.

Lossless exchanges
like every other event
can happen only at a finitely indexed step.
But there
it is excluded by logic.
An exchange of same.sized sets is lossless.
An exchange of #{#C:#C<#Cᣕᶜ} and #{#C:#C<#Cᣕᶜ}ᣕᴮᵒᵇ
is lossless.

Date Sujet#  Auteur
12 Mar 25 * The existence of dark numbers proven by the thinned out harmonic series451WM
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25 Mar 25    ii  iii  i i i i i i                       iii ii    i i      `- Re: The reality of sets, on a scale of 1 to 10 (theory of theories)1Jim Burns
26 Mar 25    ii  iii  i i i i i i                       iii ii    i `* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)6Chris M. Thomasson
27 Mar 25    ii  iii  i i i i i i                       iii ii    i  `* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)5Jim Burns
27 Mar 25    ii  iii  i i i i i i                       iii ii    i   `* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)4FromTheRafters
27 Mar 25    ii  iii  i i i i i i                       iii ii    i    +- Re: The reality of sets, on a scale of 1 to 10 (theory of theories)1Jim Burns
27 Mar 25    ii  iii  i i i i i i                       iii ii    i    `* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)2Ross Finlayson
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24 Mar 25    ii  iii  i i i i i i                       iii ii    `* Re: The reality of sets, on a scale of 1 to 10 (theory of theories)3Jim Burns
22 Mar 25    ii  iii  i i i i i i                       iii i`- Re: The reality of sets, on a scale of 1 to 101WM
22 Mar 25    ii  iii  i i i i i i                       iii `- Re: The reality of sets, on a scale of 1 to 101WM
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21 Mar 25    ii  iii  i i i i i i                       +* Re: The non-existence of "dark numbers"3FromTheRafters
22 Mar 25    ii  iii  i i i i i i                       `* Re: The non-existence of "dark numbers"58Jim Burns
16 Mar 25    ii  iii  i i i i i +* Re: The non-existence of "dark numbers"85Alan Mackenzie
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15 Mar 25    ii  iii  i i i `* Re: The non-existence of "dark numbers"3Chris M. Thomasson
15 Mar 25    ii  iii  i i `* Re: The non-existence of "dark numbers"7joes
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13 Mar 25    ii  `* Re: The non-existence of "dark numbers"4Ben Bacarisse
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12 Mar 25    +* Re: The non-existence of "dark numbers" [was: The existence of dark numbers proven by the thinned out harmonic series]2FromTheRafters
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