Re: Replacement of Cardinality

Am Sat, 27 Jul 2024 12:16:24 +0000 schrieb WM:

Le 27/07/2024 à 13:27, Richard Damon a écrit :

On 7/27/24 7:13 AM, WM wrote:

Le 27/07/2024 à 04:23, Richard Damon a écrit :
 

By your logic, if you take a set and replace every element with a
number that is twice that value, it would by the rule of construction
say they must be the same size.

 
That is true in potential infinity. But I assume actual infinity.

>

So, what part is not true?

In potential infinity there is no ω.

Neither is there in actual infinity.

Are you stating that replacing every element with another unique
distinct element something that make the set change size?

Yes they are.

In actual infinity the number of elements of any infinite set is fixed.
Doubling all elements of the set ℕ U ω = {2, 4, 6, ..., ω} yields the
set {2, 4, 6, ..., ω, ω+2, ω+4, ..., ω*2}.

I wonder how you get the second infinity. What is the preimage of all
the omegas?

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.