Dfeldmann

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Salut, Denis. It seems no one has greeted you recently. Charles Matthews (talk) 17:07, 27 November 2009 (UTC)

2^omega=omega ?

Bonjour,

J'aimerais beaucoup avoir la preuve de 2^ω=ω, en se basant sur la définition "de base" de l'exponentiation (celle qui passe par la définition de α^(β), et non par récurrence transfinie).
En effet, en reprenant la définition en question, 2^(ω) serait égal à l'ensemble des fonctions indicatrices de ω (les f:ω→{0,1}), qui ont un support fini. Cela ressemble beaucoup à l'ensemble des parties de ω !!

Probablement la nuance réside justement dans le fait que les fonctions de 2^(ω) sont à support fini, et j'aimerais donc beaucoup avoir des éclaircissements !
(Aussi, si l'explication réside justement dans la question de support fini, pourquoi l'exponentielle pour les ordinaux limite est-elle définie ainsi et non pas "comme" l'exponentielle pour les cardinaux ?)

En tout cas merci à vous et aux autres coéditeurs de l'article qui est vraiment excellent (bien supérieur à la version anglaise par exemple) !

Lajarre (talk) 15:57, 27 August 2012 (UTC)

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