A question about the definition of 'set'

[xxxx0xxxx]

That doesn't answer the question...

Well,

having failed to answer your question in which you replaced my word "model" with your word "rephrased," and shown why mathematics is very much like arguing "how many angels can fit on the head of pin?", I return to my original statement to the OP:

A \mbox{ is a set} \Leftrightarrow \exists z (z \in A \vee A = \emptyset)

without any of the encumbrances peculiar to a particular theory of sets.

Best regards to all...

except those who absolutely have to have the last word...

 

[micromass]

Well,

having failed to answer your question in which you replaced my word "model" with your word "rephrased,"

OK, sorry. Then provide a proof why ZF can be seen as model of other set theories? Or whatever it is you meant.

and shown why mathematics is very much like arguing "how many angels can fit on the head of pin?"

Let me remind you how mathematics works: we work with clear definitions and we prove things. Therefore, if we make a statement, then the statement should be precise and provable. If you actually think that mathematics is like arguing "how many angels can fit on the head of a pin", then I'm sorry but you haven't understood mathematics at all.

I return to my original statement to the OP:

A \mbox{ is a set} \Leftrightarrow \exists z (z \in A \vee A = \emptyset)

Doesn't work in NBG.

except those who absolutely have to have the last word...

It's not about having the last word, it's about correct obviously false statements.

 

[Hurkyl]

Ah, we've moved onto the "try to drown them in a deluge of material without any explanation or attempting to connect it to the issue at hand" stage of crackpottery. I think now's a good time to close it.