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

On 24.09.2024 18:49, Jim Burns wrote:

WM's argument goes something like this:
 🛇⎛ The set of unit.fractions exists.
🛇⎜ No _identifiable_ unit.fraction is its second end.
🛇⎜ (axiom) All sets have two ends.

Not an axiom but the fact that below zero there is no unit fraction proves the lower end.

🛇⎜ The second end of the unit.fractions exists
🛇⎝ but it is _not identifiable_
 There is plenty to correct in that,
but I think WM's cornerstone.error is
how he thinks axioms work.

I think that mathematics of fractions is correct.
It contains ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 from which follows that never two different5 fractions sit upon each other. From NUF(0) = 0 the smallest unit fraction follows immeditely, From it the largest natural number.
Regards WM