# Definition talk:Class Membership

Can we reword this? "In an effort to increase the rigor ..." presupposes something which has gone before in a linear exposition in a book. If there is something which has gone before this, it needs to relate directly to that, and also be worded so as to stand alone. --prime mover 00:42, 13 September 2011 (CDT)

Thanks for catching this... I have reworded the definition. -Andrew Salmon 00:45, 13 September 2011 (CDT)
Okay, better - I'll give it a rewrite later when I have a less hurried head on. --prime mover 01:38, 13 September 2011 (CDT)
... in fact, since this discusses proper classes only, should it not say something like that in the page name? Cutting out all the waffle, we can see that this page could be reduced to a page called "Definition:Proper Class" defining a "proper class" as being something which fulfils the line of set-theory notation. Job done.
Or have I missed something? --prime mover 01:43, 13 September 2011 (CDT)
Well, the whole point of the definition is to have a working relation for membership where both sets and proper classes can be substituted simply in a way that makes sense and resolves thinking in naive set theory (if that makes sense). Really, the behavior for proper classes is quite simple (proper classes can't be elements by the definition, which is exactly the behavior we want to establish), and the behavior for sets stays the same. -Andrew Salmon 01:50, 13 September 2011 (CDT)
Yes fair enough, but the contents of the page seem solely to deal with membership of a proper class, which doesn't seem to reflect what's in the page title. --prime mover 03:26, 13 September 2011 (CDT)

## Move to Theorem

With the recent material added, this definition should be moved to a theorem, as per Takeuti. --Andrew Salmon 16:04, 7 August 2012 (UTC)

Would Characterization of Class Membership suffice? Alternatively, it can be merged into Definition:Class/Zermelo-Fraenkel. --Lord_Farin 16:17, 7 August 2012 (UTC)