On Sunday, May 4, 2014 1:51:39 PM UTC-7, muec...@rz.fh-augsburg.de wrote: > On Sunday, 4 May 2014 19:59:59 UTC+2, Zeit Geist wrote: > > > For example, let S be the Set of Indesceribles in R. > > Let G be the Set of all 10-tuples of S. > > Then, for any H e G, S\H exists. > > Now, given two Elements of G, we can't tell them apart. > > But this doesn't violate any Axiom. > > Axiom of extensionality. How do you know whether you have two different elements of G?
Ass, I know what the Axiom of Extensionality is!
Choose a e G and b e G. Does a = b? We don't know. If we can show that a and b contain different Elements, then ~( a=b ). However, we can't show this, but this doesn't Violate Extensionality.
Extensionality does Not say that given any two Set we must know whether or Not a = b.
> But that is matheology. In mathematics we don't accept elements that cannot appear in mathematical discourse, dialogue, or monologue (i.e., which cannot be thought of).
I was just speaking of them. How do they not appear in Discourse?
Why don't you get a book on Set Theory and learn something about L and 0#.