# Definition talk:Cardinal

## Set of all sets

... is it technically accurate to term the "set of all sets" as an "impossibility"? I would be tempted to say "... leads to a logical contradiction". Or is it okay to define a concept that leads to such a contradiction as an "impossibility"? If so, then it might be worth adding such a definition of "impossibility". My personal view is that the word "impossibility" is too glib and carries a lot of unnecessary natural-language "baggage", so to speak. What do you think? --prime mover 08:11, 15 May 2011 (CDT)

It is kind of vague, I'll change it, and also add a page about the set of all sets, since it's not quite Russell's paradox. --Linus44 08:34, 15 May 2011 (CDT)
The definition does not match the note. The "cardinal as an equivalence class" is actually a different concept, where the cardinality of $S$ is the (proper) class of all sets equivalent to $S$. --Dfeuer (talk) 15:58, 30 April 2013 (UTC)