On Monday, 5 May 2014 00:32:01 UTC+2, Zeit Geist wrote:
> Choose a e G and b e G. > > Does a = b? We don't know.
Then you have not sets but only placeholders. > > 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.
But it does show that we have not sets that we know but only variables like x and y. Unless you know what x and y are, you have not two real numbers but only two placeholders. Can you understand that? >
> Extensionality does Not say that given any two Set we must know whether or Not a = b.
For given sets we know this. For placeholders, we don't, but they are not sets.