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

On 11/4/24 6:04 AM, WM wrote:

On 03.11.2024 22:21, Richard Damon wrote:

On 11/3/24 9:09 AM, WM wrote:

On 03.11.2024 13:13, Richard Damon wrote:
>

I *CAN* prove for every x in (0, 1], which is what I claimed.
>

You cannot prove that ℵo unit fractions occupy at least ℵo points?

>
Since there are Aleph_0 rational points in ANY finite length of the number line

 But not for every point x > 0. ℵo unit fractions occupy at least ℵo*2^ℵo points, hence more than ℵo points. Your assertion is true only for every point that you can define. But you cannot define points between the first ℵo unit fractions.
 Regards, WM
  

Yes, for every point x > 0, there are Aleph_0 unit fractions below it.
I showed them to you, so you know you are lying, because you don't believe your eyes.
We can define EVERY existing real value. We have definitions for them.
Therefore, your numbers that we cna not define, are not real numbers.
Your logic is based on the assumption of the existance of things that do not exist, which blows your logic up, as well as your mind.
Your "darkness" is just the void left after that explosion.