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

Am Mon, 07 Oct 2024 10:47:25 +0200 schrieb WM:

On 06.10.2024 18:48, Alan Mackenzie wrote:

WM <wolfgang.mueckenheim@tha.de> wrote:

On 06.10.2024 15:59, Alan Mackenzie wrote:

WM <wolfgang.mueckenheim@tha.de> wrote:

 

All unit fractions are separate points on the positive real axis,
but there are infinitely many for every x > 0.
That can only hold for definable x, not for all.

Poppycock!  You'll have to do better than that to provide such a
contradiction.

It is good enough, but you can't understand.

I do understand.  I understand that what you are writing is not maths.
I'm trying to explain to you why.  I've already proved that there are
no "undefinable" natural numbers.  So assertions about them can not
make any sense.

You have not understood that all unit fractions are separate points on
the positive axis. Every point is a singleton set and could be seen as
such, but it cannot. Hence it is dark.

Why can some points not be „seen” as a singleton set?

  Hint: Skilled mathematicians have worked on trying to
prove the inconsistency of maths, without success.

What shall that prove? Try to understand.

It shows that any such results are vanishingly unlikely to be found by
non-specialists such as you and I.

Unlikely is not impossible.

Nothing is impossible…

Try only to understand my argument. ∀n ∈ ℕ: 1/n - 1/(n+1) > 0. How can
infinitely many unit fractions appear before every x > 0?

You are getting confused with quantifiers, here.  For each such x,
there is an infinite set of fractions less than x.  For different x's
that set varies.  There is no such infinite set which appears before
every x > 0.

The set varies but infinitely many elements remain the same. A shrinking
infinite set which remains infinite has an infinite core.

Here is your essential misunderstanding: there is no mysterious Something
that makes a set infinite. It is infinite because it is not finite, has
no natural number as its size.

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.