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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: Contradiction of bijections as a measure for infinite sets
Date: Tue, 9 Apr 2024 15:47:11 -0700
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On 4/9/2024 5:22 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. Multiplication by 2 creates numbers beyond ω, or there 
> would be numbers immune to multiplication.

moron.