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

On 30.09.2024 21:51, Jim Burns wrote:

On 9/30/2024 2:54 PM, WM wrote:

NUF(0) = 0 and NUF(1) = ℵo.

 ℵ₀ is the cardinality of
cardinalities which increase by 1

Yes.

 If ℵ₀ is any
cardinality which increases by 1

No.

Therefore,
ℵ₀ does not increase by 1.

Yes.

 

∀n ∈ ℕ: 1/n - 1/(n+1) > 0
shows that at

 ...no unit.fraction...
 

no point x NUF can increase by
more than one step 1.

 0 is not a unit.fraction.

That proves NUF(0) = 0.

 

It is fact with your set too.
I am not responsible.

 Also,
you are not correct.

What is incorrect?

No reason even to care about
mathematical basic truths like
∀n ∈ ℕ: 1/n - 1/(n+1) > 0 ?

 ∀n ∈ ℕ: 1/n  >  1/(n+1) > 0
 ∀n ∈ ℕ: 1/n isn't first unit.fraction.

You should understand that NUF cannot increase by more than 1 and cannot start with more than 0 at 0. Do you understand that?
Regards, WM