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

On 10/3/24 2:25 PM, WM wrote:

On 02.10.2024 22:07, Jim Burns wrote:

On 10/2/2024 7:12 AM, WM wrote:

On 01.10.2024 22:05, Jim Burns wrote:

>

For every nonzero distance d from 0
there are ℵ₀.many unit.fractions closer than d

>
That means
there is no d by what
you can distinguish ℵ₀ unit fractions?

>
You (WM) require us to guess
what you mean by 'distinguish'.

 You distinguish two unit fractions 1/n and 1/m if you place a point in distance d from 0 between them: 1/n < d < 1/m.

>
There is no d between
ℵ₀.many.smaller.unit.fractions and
slightly.fewer.than.ℵ₀.many.smaller.unit.fractions.

 That means you cannot distinguish ℵ₀ smaller unit fractions.
 Regards, WM

Sure we can, we just can't find any that have less than Aleph_0 numbers below them since those numbers don't exist.
Your logic just can't handle numbers like Aleph_0, and thus has exploded your brain when you made it try.