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NNTP-Posting-Date: Thu, 11 Apr 2024 00:39:21 +0000
Subject: Re: Contradiction of bijections as a measure for infinite sets
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Wed, 10 Apr 2024 17:39:25 -0700
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On 04/10/2024 01:13 PM, Jim Burns wrote:
> On 4/10/2024 1:57 PM, WM wrote:
>> Le 09/04/2024 à 20:27, Jim Burns a écrit :
>>> On 4/9/2024 8:22 AM, WM wrote:
>>>> Le 09/04/2024 à 01:54, Jim Burns a écrit :
>>>>> On 4/8/2024 9:55 AM, WM wrote:
>>>>>> Le 07/04/2024 à 21:47, Jim Burns a écrit :
>
>>>>>>> The successor operation is closed in
>>>>>>> the natural numbers.
>>>>>>
>>>>>> For visible numbers only.
>>>>>
>>>>> Visibleᵂᴹ or darkᵂᴹ,
>>>>> k is a natural number  :⟺
>>>>> k=0 ∨ ∃⟦0,k⦆: ∀i ∈ ⟦0,k⦆: i⁺¹ ∈ ⦅0,k⟧
>>>>
>>>> Not correct if
>>>> there are all natural numbers such that
>>>> no further one exists below ω.
>>>
>>> You seem to be saying:
>>> | Not correct if
>>> | not all natural numbers have
>>> | a further one below ω
>>
>> All further numbers are multiplied too.
>
> ω is the first.infinite.ordinal.
>
> The numbers.before.ω are all and only
> 0 and
> any number.after.0 k such that
> k and all non.0 numbers.before.k
> have predecessors.
>
>
> No number k⁺¹ exists such that
> k and all non.0 numbers.before.k
> have predecessors
> but NOT
> k⁺¹ and all non.0 numbers.before.k⁺¹
> have predecessors
>
> Thus,
> no number.before.ω k exists such that
> k⁺¹ is NOT a number.before.ω.
>
>
> No numbers.before.ω k,m⁺¹ exists such that,
> k+m is a number.before.ω
> but NOT
> k+m⁺¹ = (k+m)⁺¹ is a number.before.ω.
>
> Thus,
> no numbers.before.ω k,m exist such that
> k+m is NOT a number.before.ω.
>
>
> No numbers.before.ω k,m⁺¹ exists such that,
> k⋅m is a number.before.ω
> but NOT
> k⋅m⁺¹ = (k⋅m)+k is a number before ω
>
> Thus,
> no numbers.before.ω k,m exist such that
> k⋅m is NOT a number.before.ω.
>
>
>>> In other words [1]:
>>> | Not correct if
>>> | ω is finiteⁿᵒᵗᐧᵂᴹ.
>>
>> Not correct if
>> there is no free space between ℕ and ω.
>
> ℕ = ⟦0,ω⦆
>
> ω is after Avogadroᴬᵛᵒᵍᵃᵈʳᵒ
> Avogadroᴬᵛᵒᵍᵃᵈʳᵒ = 6.02214076E23⁶ᐧ⁰²²¹⁴⁰⁷⁶ᴱ²³
> and after any other number such that
> it and all non.0 numbers.before.it
> have predecessors.
>
> Infiniteⁿᵒᵗᐧᵂᴹ is different.
>
>

You know, some people have that Avogadro's number,
is sort of a _running_, constant.

What I mean by that is that NIST CODATA every few
years arrives at the current values according to
the energy and configuration of experiment, and,
some of the constants are _running_ in the energy
and configuration of experiment, it results they
get not only more precise, even actually, _smaller_.

Or, you know, larger.

(Yeah, I know I've said that a bunch of times,
yet so few people seem to know.)

Law(s) of large numbers are various.