Re: Contradiction of bijections as a measure for infinite sets

Liste des GroupesRevenir à s math 
Sujet : Re: Contradiction of bijections as a measure for infinite sets
De : richard (at) *nospam* damon-family.org (Richard Damon)
Groupes : sci.math
Date : 05. Apr 2024, 12:32:36
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <uuongk$4qfr$1@i2pn2.org>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
On 4/5/24 4:56 AM, WM wrote:
Le 04/04/2024 à 15:22, Richard Damon a écrit :
On 4/4/24 9:07 AM, WM wrote:
 
It doesn't, Bijections are always between two DISTINCT sets, not a set and a piece of itself thought of as a set.
>
"In mathematics, a set A is Dedekind-infinite (named after the German mathematician Richard Dedekind) if some proper subset B of A is equinumerous to A. Explicitly, this means that there exists a bijective function from A onto some proper subset B of A." Wikipedia.
 
Right, but that "Proper Subset" is considered as an independent item, not as just pieces of the original set.
 Nevertheless it is a piece of the original set.
 Regards, WM
No, its ELEMENTS are part of the original set.
The set of Natural Numbers does not have as a member of it, the set of Even numbers, only all the Even numbers as members of it.

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