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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 15:59:19 -0700
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On 4/9/2024 3:42 PM, Richard Damon wrote:
> On 4/9/24 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. Multiplication by 2 creates numbers beyond ω, or there 
>> would be numbers immune to multiplication.
>>
>> Regards, WM
> 
> Nope, because there isn't a "last" natural number, so the statement "no 
> further one exists" isn't factual, but your false logic of using logic 
> that only works on finite sets on an infinite set.
> 
> Multiplying ANY Natural numbers (which are all finite) by two, results 
> in another finite Natural Number.

Right! And this new natural number is already in the set of all natural 
numbers. Why can't WM get this! God damn.