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

On 9/25/2024 12:57 PM, Ross Finlayson wrote:

On 09/25/2024 12:35 PM, Chris M. Thomasson wrote:

On 9/25/2024 8:26 AM, WM wrote:

On 25.09.2024 13:54, Richard Damon wrote:

On 9/24/24 3:38 PM, WM wrote:

On 24.09.2024 10:00, joes wrote:

Am Sun, 22 Sep 2024 15:28:38 +0200 schrieb WM:

>

Really existing sets of real unit fractions have two ends.

What is „an end”?

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An end is where nothing follows.

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And thus the lower end of the numbers x > 0 would be 0, a value not
in the set, as the set doesn't have a lower end in it.

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If it is a set (actual infinity), then the set has a smallest member.
But that is hard to understand.

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That is why there is no smallest positive real or unit fraction.

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It is easier to understand with unit fractions. But most
mathematicians are too stupid even for this obvious fact.

>
If you truly believe in a smallest unit fraction and/or largest natural
number, well.... You are totally whacked out. You say most
mathematicians are too stupid. I think that its you projecting yourself
on others? ;^)

 Number theorists, where it's their theory, of numbers,
sometimes do indeed posit a "point at infinity", as
a member, or "one-point compactification", of what
are their "natural numbers".

A point at infinity is "usually" a point to gain a perceptive from. It is a _finite_ point that is simply called infinity. We can say the point at infinity is 100 units down the z-axis, off in the distance so to speak. We can use it to draw lines in perspective drawing. This does not mean that infinity it finite at all. There is no smallest unit fraction and there is no largest natural number. Ever look down a long road and it seems to project itself into a point? This does not mean there is a smallest unit fraction at all...

 That "the naturals are compact" is along the lines
of like "the reals are projectively well-ordered"
with regards to that there are models of the integers,
where it is so.
 Where it is so, ....
 Then with regards to theories of atomism while in the
meso-scale things are divisible, has that it's among
classical theories and complementary duals and you'd
be well advised to be aware of them in settings where
the topics are science, physics, mathematics, logic, ....