Sujet : Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)
De : richard (at) *nospam* damon-family.org (Richard Damon)
Groupes : sci.logicDate : 13. Dec 2024, 03:29:26
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <748bc2d4a21768ea7d5ccb1bb4557a9d400da0c8@i2pn2.org>
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User-Agent : Mozilla Thunderbird
On 12/12/24 4:57 PM, WM wrote:
On 12.12.2024 14:59, joes wrote:
What Richard meant: do not confuse the set being mapped with the one being
mapped onto.
>
I don't. D = {10n | n ∈ ℕ} is the set being mapped. The set D being mapped does not change when it is attached to the set ℕ being mapped in form of black hats.
Regards, WM
And so, which element of which set didn't get mapped to a member of the other by the defined mapping?
Remember, the equinumerous requirements was just that their exist *A* mapping that do it, not that every attempted mapping works.
To insist on that, is to deny an essential property of infinity, and thus prove that you logic system can't have infinite sets.