User talk:Dfeldmann

Hello Dfeldmann! Welcome to Wikipedia! Thank you for your contributions to this free encyclopedia. If you decide that you need help, check out Getting Help below, ask me on my talk page, or place {{helpme}} on your talk page and ask your question there. Please remember to sign your name on talk pages by clicking

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

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)[reply]

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