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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Tue, 1 Oct 2024 19:29:21 +0200
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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