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

On 10/23/24 10:46 AM, WM wrote:

On 23.10.2024 13:37, Richard Damon wrote:

On 10/22/24 12:12 PM, WM wrote:

On 22.10.2024 18:03, Jim Burns wrote:

 

∀n ∈ ℕ:  2×n ∈ ℕ

>
Not if all elements are existing before multiplication already.

>
IF not, then your actual infinity wasn't actually infinite

 It is infinite like the fractions between 0 and 1. When doubling we get even-numerator fractions, some of which greater the 1.

But from 0 to 1 isn't an infinite distance, thus doubling can put you out of that bound, and we can find a specific definaable number where that happens. It has a finite value for the upper limit.
At 1/2, we double to hit the boundry.
But, with the Natual Numbers, there isn't a value that is 1/2 of the "highest value" since there isn't a highest number that is a Natural Number, since every Natural Number has a successor that is higher.

 

Your "actual infinity" seems to be just an unimaginably large value, not infinite, as your actual infinity has an end, it has an element without a successor, so it isn't the set it claims to be.

 The completed infinite cannot avoid to be complete. But it is infinite because the end cannot be determined because of the dark domain.

No, the end cannot be determined, because it isn't there.
There is nothing about being complete that means it needs to have an "end", that is just your broken finite thinking that has blown your logic to smithereens.
Your "darkness" is just a method you use to hide your errors, but it can't actually be defined in a way to be used.
Sorry, you are just proving how stupid you are.

 Regards, WM