Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

On 10/20/24 3:44 PM, WM wrote:

On 20.10.2024 21:31, Richard Damon wrote:

On 10/20/24 3:15 PM, WM wrote:

 

When a set of numbers is mapped then the number of numbers remains fixed.
>

Right, so the "ALeph_0" Natural Numbers were mapped to the Even Natural Numbers, a set with exactly that same size, which is also a proper subset of it.

 I did not talk about cardinality which is nonsense but about the real number of elements, Cantor called it reality.
 Regards, WM
 

And the number of elements is Aleph_0. The "number of elements" is what Cardinality measures.
The problem comes when your set has more elelemnts than you have a number to rerpesent it, so "Number of ELements" becomes in incorrect term, until you extend the number system to include the infinite cardinal numbers to allow you to HAVE a "number" to use to express the "number of elements" in such a set.