Valloud Andres <Andres.Valloud at oya.state.or.us> wrote:
	When you write x in x\x or xUx, you don't refer to the actual set,

Yes you do.  That's how mathematics works.

	you refer to a definition.

No you don't.

	You can refer to a definition because you wrote something like
	
		x = {e | e has some property}
		y = {e1, ..., en}
	
Not often.  In the case of the first, not _ever_ in modern set theory.
That's what they call an 'impredicative' definition and it leads to well
known paradoxes.

More typically, in a theorem or a program, some of the sets are *PARAMETERS*
whose definitions you do NOT have access to.

Similarly, in the Smalltalk case we are considering, the x and y variables
are extremely likely to be parameters whose defining code may not yet have
existed at the time we wrote ours.

	Named "sets" are just shorthands for their definitions,

No, that's classes.  Read a book on modern set theory.  You will discover
that almost no sets have definitions.  (Simple reason:  definitions are
countable, sets aren't.  It's not even that there are infinitely many more
sets than definitions, it's worse than that.)

(Aren't I lucky that I've been revising set theory recently?)