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

On 9/25/24 11:28 AM, WM wrote:

On 25.09.2024 13:58, Richard Damon wrote:

On 9/24/24 4:37 PM, WM wrote:

 

The alternative is that the unit fractions keep getting closer and closer without limit.

 Either they occupy one point or NUF will distinguish them.
 Regards, WM

No, they are all different, and NUF just jumps because there is no first point for it to count at.
Or, are you admitting that 1/n - 1/(n+1)  might be zero in your logic.
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, and never increases after that, as once it get to Aleph_0, we have the fact that Aleph_0 + 1 is still Aleph_0.
Defining something based on non-existant entities isn't good for a basis of a logic system.