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

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'.
There is no d between
ℵ₀.many.smaller.unit.fractions and
slightly.fewer.than.ℵ₀.many.smaller.unit.fractions.
...because
∀ᴿd>0:
⎛ u(k) = ⅟⌈k+⅟d⌉
⎜ u: ℕ → (0,d]: one.to.one
⎝ NUF(d) = |u(ℕ)| = |ℕ| = ℵ₀
But finite sets don't act like that!
Right.
Finite sets don't act like that.
Assuming all sets are finite leads to gibberish.