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

On 08.09.2024 22:11, Richard Damon wrote:

On 9/8/24 3:52 PM, WM wrote:

On 07.09.2024 16:51, Richard Damon wrote:

On 9/7/24 9:45 AM, WM wrote:

>

Because ℵo unit fractions have ℵo gaps. We can use one of the gaps as x  > 0.
>

But you started with that x, so it was fixed to begin with.

>
No, it is the size of one of the gaps between two adjacent unit fractions, ℵo of which are claimed to fit into (0, x).

 So it is the size of *ONE* of the gaps, you need to choose which one, as all the gaps are different sizes.

And all gaps are occupied by the unit fractions. Hence every gap is too small.

 Remember, just as there is no smallest unit fraction, there is no smallest gap, so you can't specify choosing the smallest.
 The fact that the choice is for ANY, it requires you to actually CHOOSE one, and then we can find the Aleph_0 smaller.

No. First you claim the unit fractions with their gaps. Then I choose one of them, irrelevant which one. Each one is smaller than all.
Regards, WM