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

On 10/17/24 2:46 PM, WM wrote:

On 17.10.2024 02:18, Richard Damon wrote:

On 10/16/24 11:20 AM, WM wrote:

On 16.10.2024 13:54, Richard Damon wrote:

On 10/16/24 4:30 AM, WM wrote:

>

There is a general rule not open to further discussion:
When doubling natural numbers we obtain even numbers which have not been doubled.
In potential infinity we obtain more even natural numbers than have been doubled.
In actual infinity we double ℕ and obtain neither ℕ or a subset of ℕ.
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But that isn't actually a general rule,

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It is a general rule that doubling creates larger numbers.

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Yes, but none get larger than the domain of the Natural Numbers, the set we started from.

 When doubling natural numbers we obtain even numbers which have not been doubled.

Then your "Actual Infinity" wasn't actually infinte.
As it must contain *ALL* the Natural Numbers to be that set.
Sorry, you are just proving that your logic is just a lie as your "infinite" is just finite, because you don't know what you are talking about.

 

This just shows the unusual behavior of infinite sets.

 2n > n is always true, in finite and in infinite sets.

In FINITE or ORDINAL systems, and there 2n will be in the same actually infinite set as n.
In Infinte Cardinal spaces (like Aleph_0 is in) 2n == n

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you assume that the actual infinity is finite

 No, it is simply complete. Therefore not for all n 2n can be a natnumber.

And if it *IS* complete, it contains every Natural Number, and thus since 2*n IS a Natural Number it is in the complere set of Natural Numbers which we started from.
Trying to cal them "natnumbers" is just a ruse to hid your lies.
Your concept of "Actual Infinity" is actually infinite, and you are just showing that you are just a stupid liar that doesn't understand what he talks about,

 Regards, WM