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

On 9/21/2024 9:43 AM, WM wrote:

On 20.09.2024 21:26, Jim Burns wrote:

On 9/20/2024 2:10 PM, WM wrote:

On 20.09.2024 19:51, Jim Burns wrote:

Put pencil to paper and draw two curves which cross.
There is a point at which the curves intersect.

>
This proves that no line has gaps.

>
A point (hypothetically) next to 0
has an absence of points between it and 0
>
No such absence of points exists.

>
You cannot see the point because it is dark.

WWMB (what we mean by) ℝ\ℚ completes WWMB ℚ
⎛ Each split of WWMB ℚ not situated by
⎜ a point of WWMB ℚ
⎜ is situated by a point of WWMB ℝ\ℚ
⎜
⎜ ∀S ⊆ ℚ:
⎜⎛ {} ≠ S ᵉᵃᶜʰ<ᵉᵃᶜʰ ℚ\S ≠ {}  ∧
⎜⎝ ¬∃q ∈ ℚ:  S ᵉᵃᶜʰ≤ q ≤ᵉᵃᶜʰ ℚ\S
⎝ ⇒ ∃r ∈ ℝ\ℚ:  S ᵉᵃᶜʰ< r <ᵉᵃᶜʰ ℚ\S
WWMB ℝ no.more.than.completes WWMB ℚ
⎛ Each point of WWMB ℝ ⊇ ℚ situates
⎜ a split of WWMB ℚ
⎜
⎜ ∀r ∈ ℝ:
⎝ ∃S ⊆ ℚ: S ᵉᵃᶜʰ≤ r ≤ᵉᵃᶜʰ ℚ\S
If what you say isn't about WWMB ℝ and ℚ,
then what you say isn't about WWMB ℝ and ℚ.