Definition talk:Class (Class Theory)

Classes vs. Sets
It seems like a lot of potential ambiguity / paradoxes arise from a lack of verbal syntax as far as referring to classes vs. sets. From how I understand it, when we talk about sets, we are only about elements of the universe of discourse, no? And classes are collections of these sets. However, for example, the definition of a singleton refers to them as "sets" which seems to presuppose the existence of sets that contain exactly one element (which requires the axiom of pairing or axiom of power set to prove in reality). -Andrew Salmon 17:28, 12 September 2011 (CDT)


 * What's your point? --prime mover 00:37, 13 September 2011 (CDT)


 * Only when things have been proven to be elements of the universe of discourse should they be considered and referred to as sets...this, however, is easy to tie up. -Andrew Salmon 00:43, 13 September 2011 (CDT)

Removed Comment
I have removed the comment about ZF and Von Neumann-Gödel-Bernays set theory, because ZF does allow the use of classes. The difference between the two systems is that you can quantify over classes in NGB, but you cannot in ZF. --Andrew Salmon 03:37, 7 August 2012 (UTC)