Re: Replacement of Cardinality

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

But that resultant set is the evens, which can also be shown by your logic to have less elements than the Natural Numbers they were made from by doubling,

 So it is.

WHich shows the logic to be wrong.

 Regards, WM