Re: Replacement of Cardinality

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.

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

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}.
Regards, WM