Sujet : Re: More complex numbers than reals?
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.mathDate : 18. Jul 2024, 12:18:04
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <a1e83f09-e030-4da5-aea9-4c716c6f020d@att.net>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
On 7/17/2024 1:57 PM, WM wrote:
Le 17/07/2024 à 19:11, Jim Burns a écrit :
On 7/16/2024 3:33 PM, WM wrote:
What about the infinitely many numbers
which are remainimg from E(1)?
>
None of them remain in
all.infiniteⁿᵒᵗᐧᵂᴹ (all) end segments.
>
What remains to keep the endsegments infinite?
| For each number, there is a number after
proves false
| There is a number after all numbers.
An infiniteⁿᵒᵗᐧᵂᴹ end segment
common to all infiniteⁿᵒᵗᐧᵂᴹ end segments
not.exists.
>
Because of inclusion monotony
this is a wrong result.
You (WM) aren't referring to ℕⁿᵒᵗᐧᵂᴹ
⎛ Each j in ℕⁿᵒᵗᐧᵂᴹ has in ℕⁿᵒᵗᐧᵂᴹ
⎜ non.0 j⁺¹ immediately.after j
⎜
⎜ Each non.0 k in ℕⁿᵒᵗᐧᵂᴹ has in ℕⁿᵒᵗᐧᵂᴹ
⎜ k⁻¹ immediately.before k
⎜
⎜ Each nonempty subset B ⊆ ℕⁿᵒᵗᐧᵂᴹ holds
⎝ min.B smallest in B.
…