Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (doubling-spaces)
De : noreply (at) *nospam* example.org (joes)
Groupes : sci.mathDate : 12. Nov 2024, 23:03:06
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <9fedbc85117637c89eec23847a48c589556de714@i2pn2.org>
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User-Agent : Pan/0.145 (Duplicitous mercenary valetism; d7e168a git.gnome.org/pan2)
Am Tue, 12 Nov 2024 22:38:51 +0100 schrieb WM:
On 12.11.2024 21:03, Jim Burns wrote:
On 11/12/2024 1:06 PM, WM wrote:
On 12.11.2024 17:47, Jim Burns wrote:
3) Then we could first cover all naturals and then all halves and then
all quarters and so on. But we know that already after covering all
naturals no further intervals are available.
Well, because this order has the type
omega + omega + … omega = omega*omega = omega^2.
This amounts to saying that the naturals are a subset of the rationals.
It goes back to the lines (or columns) of your tired matrix.
That is not a bijection between N and Q. That doesn’t prove there is none.
-- Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:It is not guaranteed that n+1 exists for every n.