Quote by mahmoud2011
This can considered as a logic question , when I say for example there exist x such that ... . Mustn't I define some set from which x belong .
In a book of set theory it defined a binary relation as following :
A set R is a binary relation if [itex](\forall x \in R)(\exists x)(\exists y)(z=(x,y))[/itex]
The way I understand [itex]\exists x[/itex] is as following , as he is referring to any set x which exist , So we must consider some Set containing all sets , Such set doesn't exist . So what set must be considered , how must I understand this I know that we didn't mention the universal set if it is clear from context . Here , there is no Universal set . we want x to be arbitrary .
Thanks

There is no set containing all sets, but there is a class containing all sets...Mathematicians say.