Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : richard (at) *nospam* damon-family.org (Richard Damon)
Groupes : sci.mathDate : 12. Dec 2024, 01:32:21
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <4e7901e16785581d0d02a2d6474d7d2615c5fac9@i2pn2.org>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
User-Agent : Mozilla Thunderbird
On 12/11/24 9:32 AM, WM wrote:
On 11.12.2024 03:04, Richard Damon wrote:
On 12/10/24 12:30 PM, WM wrote:
On 10.12.2024 13:17, Richard Damon wrote:
On 12/10/24 3:50 AM, WM wrote:
>
Two sequences that are identical term by term cannot have different limits. 0^x and x^0 are different term by term.
>
Which isn't the part I am talking of, it is that just because each step of a sequence has a value, doesn't mean the thing that is at that limit, has the same value.
>
Of course not. But if each step of two sequences has the same value, then the limits are the same too. This is the case for
(E(1)∩E(2)∩...∩E(n)) and (E(n)).
But the limit of the sequence isn't necessary what is at the "end" of the sequence.
The end of the sequence is defined by ∀k ∈ ℕ : E(k+1) = E(k) \ {k}.
Regards, WM
None of which are an infinite sets, so trying to take a "limit" of combining them is just improper.
…