The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Using classes instead of sets
Replies: 26   Last Post: Apr 1, 2013 8:04 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Frederick Williams

Posts: 2,164
Registered: 10/4/10
Re: Using classes instead of sets
Posted: Mar 28, 2013 3:27 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply wrote:
> [...] Classes are allowed to contain other classes after all.

If X, Y are proper classes in NBG, one may not have X in Y, but one may
have X subset Y. So it depend on what 'contains' means.

> Of course, we get Russell-type paradoxes if we allow entities to contain themselves, whether the entities be sets or classes.

So by 'contain' you mean $\in$ I suppose. But the language of set
theory allows x \in x as a formula, but it doesn't allow {x | x in x} as
a set. Otoh, {x in y | x in x} is a set if y is.

[I know nothing about set theories that aren't ZF or NBG, and I know
next to nothing about those.]

When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.