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

On 10/13/2024 6:12 PM, Chris M. Thomasson wrote:

On 9/18/2024 7:31 AM, Jim Burns wrote:

On 9/18/2024 8:39 AM, WM wrote:

On 16.09.2024 19:30, Jim Burns wrote:

On 9/15/2024 3:47 PM, WM wrote:

I don't believe in gaps on the real line.

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There aren't gaps and there aren't next.numbers
in numbers.situating.splits of rationals with
countable.to.numerators.and.denominators

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So what is next instead?

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What is between one and the next?
A gap.

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With regard to a very _strict) line of thinking
(no mixing and matching), say 100% natural numbers...
There is NO "gap" between, say:
3 and 4

That aligns with WM's take on 'gap', IIRC, as
being a place something _should_ be, but _isn't_
I would be comfortable with that take,
if it were used consistently.
It would just mean that _there are no gaps_
A set is what it is, and
it _should_ not.be anything it isn't.
However (you knew 'however' was coming),
WM somehow manages to have gaps.
He keeps his dark thingummies in them.
What does WM "really" mean by 'gap'?
I strongly suspect that that is a question
for which an answer does not exist.

There is no gap in the real line.
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There is no next in the real line.
If there were, there'd be a gap.
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