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

Am 10.09.2024 um 20:35 schrieb Chris M. Thomasson:

On 9/9/2024 5:32 PM, Moebius wrote:

Am 10.09.2024 um 01:08 schrieb Chris M. Thomasson:
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Take the gap between:
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1/1 and 1/2. There are infinitely many unit fractions that are small enough to fit within that gap.

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Oh, really?! Could you name (just) o n e? :-)

 1/4?

Hmmm... 1/2 < 1/4 < 1/1
i.e. 0.5 < 0.25 < 1.
Are you sure?

I mean ... a unit fraction u such that 1/2 < u < 1/1. :-o

On the other hand, 1/2 < 1/2 + 1/4 < 1/1
i.e. 0.5 < 0.75 < 1.
But 1/2 + 1/4 = 3/4 is not a unit fraction. :-P