Re: Ordered pairs

[Piotr Rudnicki <piotr@cs.ualberta.ca>]

Adam Kolany wrote: 
> > 
> > What is the reason for having the ordered pair defined as
> > 
> > 	[x, y] = { { x,y }, { x } };
> > 
> > and not as 
> > 
> >         [x, y] = { x, {x, y} }
> 
> I think the other one would not prove: [x,y]=[u,v]=>x=y&y=u without 
> regularity axiom.

Indeed, in proving [x1,x2] = [y1, y2] implies x1 = y1 & x2 = y2 
one needs the regularity axiom.  But we have the axiom anyway. So,
what is the deal? Just elegance?


-- 
Piotr Rudnicki