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

On 10/20/24 3:50 PM, WM wrote:

On 20.10.2024 21:31, Richard Damon wrote:

On 10/20/24 10:26 AM, WM wrote:

On 20.10.2024 13:56, Richard Damon wrote:

On 10/20/24 3:48 AM, WM wrote:

>

All doubled numbers result in larger numbers. That cannot be avoided.

´

But since there isn't a "largest" number,

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There is completeness.

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Which meaning of "Completeness" do you mean?

 

For set theory, the "Completeness" of the Natural Numbers says there is a suprema of the set

 Completes means that all elements of a set are existing. The natural numbers for instance are invariable. The subset of even numbers and the subset of odd numbers are two halves having only half of the reality of the natural numbers.
 Regards, WM
 

Right, all exist, but in being infinite, that means that it doen't have an "end" and thus any logic that presumes an "end" isn't applicable.
Your problem is just that your idea of "completeness" assumes an implied finiteness, which the set doesn't have, thus, you logic can NEVER have a complete infinity, so your "actual infinity" just isn't actually infinite, but just wrong.
Your mind is just blowing up by the fact that half of an infinite set can be the same size as the whole, because Aleph_0 / 2 == Aleph_0