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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Gaps... ;^)
Date: Mon, 9 Sep 2024 15:59:53 -0700
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Between zero and any positive non-zero x there is a unit fraction small 
enough to fit in the gap. The x can even be a real that is not a unit 
fraction.

Between x and any y that is different than it (x), there will be a unit 
fraction to fit into the gap. infinitely many.... :^)

Say the gap is abs(x - y) where x and y can be real. If they are 
different (aka abs(x - y) does not equal zero), then there are 
infinitely many unit fractions that sit between them.

Any thoughts? Did I miss something? Thanks.