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

On 9/27/24 3:06 PM, WM wrote:

On 25.09.2024 19:12, Richard Damon wrote:
 

The problem is that it turns out the NUF(x) NEVER actually "increments" by 0ne at any finite point, it jumps from 0 to infinity (Aleph_0) in the unboundedly small gap between 0 and all x > 0,

 How do you distinguish them?
 Regards, WM
 

They have different values, so why can't you?
If the question is how to distinguish the VALUE of NUF(x) at different x, you CAN'T for all x > 0, as it is always the same value, even after "incrementing" it for passing a unit fraction.
You seem to have a funny-mental issue that you don't understand that different numbers ARE different, and are defined, and that infinity doesn't act the same as finite numbers, and trying to make it work the same just breaks your logic.
The problem you run into is that a "first" fraction doesn't exist, so you can't "distinguish" it, not because there is something wrong with that number, but because such a thing just doesn't exist.
The issue isn't what color is a red ball that is green, it is where do you find such a contradictory thing.
Your assumption of a "first point" after zero is just the proof of your insantity,