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

On 9/24/24 3:43 PM, WM wrote:

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
 

Except that there doesn't exist a largest natural number, BY DEFINITION, so your finite mathematics can't handle the logic you are putting it to.
SORRY, you are just showing your total ignorance of what you talk about,