Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 11/21/2024 2:21 PM, WM wrote:

On 21.11.2024 19:54, Jim Burns wrote:

On 11/21/2024 11:24 AM, WM wrote:

By what is it covered,
after all n have been proved unable?

>
⎛ n ↦ i/j ↦ n
⎜
⎜ (i+j) := ⌈(2⋅n+¼)¹ᐟ²+½⌉
⎜ i := n-((i+j)-1)⋅((i+j)-2)/2
⎜ j := (i+j)-i
⎜
⎝ (i+j-1)⋅(i+j-2)/2+i = n

>
That is not an answer.

You (WM) see it as "indistinguishable from magic".
That's a shame for your students.
⎛ Arthur C Clarke's Third Law
⎜
⎜ Any sufficiently advanced technology
⎝ is indistinguishable from magic.

Further it is only valid for
the first numbers which are followed by
almost all numbers.

ℝ⁺ points between splits of ℚ⁺
ℚ⁺ ratios of numbers in ℕ⁺
ℕ⁺ countable.to from.1
n ↦ ⟨i,j⟩ ↦ n
is valid for all of ℕ⁺ and all of ℕ⁺×ℕ⁺
ℕ⁺×ℕ⁺ → onto ℚ⁺

Never completed.

The _description_ is completed.
It's right there.
Finite sequences of claims, each of claim of which
is true.or.not.first.false
are completed.