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

On 9/12/2024 7:39 AM, WM wrote:

On 12.09.2024 07:03, Jim Burns wrote:

On 9/11/2024 3:53 PM, WM wrote:

But you claim that if β exists, then ½.β exists.
And if ½.β exists, then β/4 exists, and so on.

>
There's a proof.

>
It is based on an axiom which
does not reproduce real mathematics.

It is based on
⎛ each positive.integer j having
⎜ first.after positive.integer j+1 and
⎜ last.before positive.integer j-1
⎜ (except min.positive.integer 1 with first.after 2)
⎜ and
⎜ each nonempty set A of positive integers holding min.A
⎜
⎜ And each rational number being
⎜ the difference of ratios j/k-j′/k′ of positive integers
⎜
⎜ And each real number x being
⎜ situated at a split S ⊆ ℚ of all rational numbers.
⎝ {} ≠ S ᵉᵃᶜʰ< x ≤ᵉᵃᶜʰ ℚ\S ≠ {}
If you (WM) aren't talking about those,
then you aren't talking about those.
⎛ Kits, cats, sacks, wives:
⎝ how many were going to St. Ives?

But we need not use sets at all
if we use the points.

>
If you use points as sets, expect gibberish.

>
Use points *as points* and
investigate their properties.

If you decide beforehand
what your "investigation" will "reveal",
expect whatever _seemed obvious_ at first
to devolve into gibberish.
You are a finite being.
⎛ Expecting infinity to be unsurprising
⎜ is like
⎜ traveling to Outer Mongolia and
⎝ expecting everyone there to speak perfect German.
Infinity is foreign.
Foreign isn't uninvestigatable,
but it also isn't same.as.it.always.was.

For each point x in (0,1]: 0 < x/2 < x
No point exists between 0 and (0,1]

>
Nevertheless (0,1] has a smallest point.
It is dark.
Where no point is, there is no interval.
Interval-ends without points are matheology.

"Obvious" has devolved into gibberish.