Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

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.