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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Wed, 25 Sep 2024 13:12:07 -0400
Organization: i2pn2 (i2pn.org)
Message-ID: <68ff21abb8e0f40ff2d435fa2077b9f44c5a55b3@i2pn2.org>
References: <vb4rde$22fb4$2@solani.org> <vc1uu8$u3ec$9@dont-email.me>
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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.