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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
Date: Sat, 11 Jan 2025 11:49:13 -0500
Organization: Peripheral Visions
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joes explained :
> Am Sat, 11 Jan 2025 09:09:34 -0500 schrieb FromTheRafters:
>> joes laid this down on his screen :
>>> Am Sat, 11 Jan 2025 11:04:56 +0100 schrieb WM:
>>>> On 11.01.2025 01:28, Richard Damon wrote:
>>>>> On 1/10/25 4:48 PM, WM wrote:
>>>>>> On 10.01.2025 21:08, Jim Burns wrote:
>>>>>> 
>>>>>>> Where OUR infinityⁿᵒᵗᐧᵂᴹ "doesn't work",
>>>>>>> it's you who's saying it doesn't work,
>>>>>> You are inconsistent. You claim that all natural numbers are an
>>>>>> invariable set. But when all elements are doubled then your set
>>>>>> grows,
>>>>>> showing it is not invariable. That is nonsense.
>>>>> But the set doesn't grow.
>>>>> Which element is in the doubled set that wasn't there in the first
>>>>> place?
>>>> The number of elements remains constant. All odd numbers of ℕ are
>>>> deleted. That implies that new even numbers are added.
>>> Nope. This is all just your conception of Aleph_0 as finite. It does
>>> not behave like that. All countable sets are bijective to each other.
>> All of the smallest inductive countably infinite sets. :)
> If that was a joke, I didn't get it. Please enlighten me?

Well, {a,b,c} is a countable set. Also, {w,x,y,z} is a countable set. 
these two countable sets do not have a bijection. "All countable sets 
are bijective to each other." is overstated.