Re: 2N=E

On 10/26/2024 11:55 AM, WM wrote:

On 26.10.2024 01:18, Jim Burns wrote:

On 10/25/2024 3:07 PM, WM wrote:

Relevant are only provable mathematical facts:

>
Provable:
⟦0,n⟧ ⊂ ⟦0,ω⦆  ⇔  ⟦0,n+n⟧ ⊂ ⟦0,ω⦆

>
True for all natnumbers you can conceive of.

True for all finite ordinal which are finite ordinals.
What you can conceive of is irrelevant to that.
A finite ordinal is predecessored or 0  and
  each of its priors is predecessored or 0.
An ordinal is successored.
A set of ordinals  is minimummed or {}

When the density is halved
the covered interval is doubled.

>
Provable:
2× : ℕ → 𝔼 : one.to.one
𝔼 = 2×(ℕ) ⊂ ℕ

>
Only for natnumbers you can conceive of.

True for all finite ordinal which are finite ordinals.
What you can conceive of is irrelevant to that.

Lossless exchanges do never lose the exchanged.

>
Provable:
|𝔼| = |ℕ\𝔼| = |ℕ|

>
Only for natnumbers which have
almost all natnumbers as successors.

'Infinite' does not mean
what you want it to mean.
Each finite ordinal has
almost all finite ordinals as successors.