Re: Replacement of Cardinality

On 8/4/24 11:23 AM, WM wrote:

Le 03/08/2024 à 17:56, Richard Damon a écrit :

On 8/3/24 10:30 AM, WM wrote:

 

But there is not even an eps that separates half of all unit fractions.

>
Because such a question is meaningles, as there isn't a finite number that is half of the count of unit fractions.

 If there are all, then there is half of all.
 Regards, WM
 

But half of aleph_0 is just aleph_0, so doesn't actually get smaller.
That is how the logic of infinite sets works.
The "even" numbers are in once sense 1/2 the size of the Natural Numbers by dropping all the odds, but are also the same size by doubling each Natural Number.
Yes, that seems counter-intuitive, but that is just the math of infinite numbers.