- #1
Berrius
- 19
- 0
Homework Statement
Prove a set which contains all of it's subsets doesn't exist.
The Attempt at a Solution
Suppose such a set P exists. P := {x | x [itex]\in[/itex] [itex]\wp[/itex](x)}.
P [itex]\in[/itex] [itex]\wp[/itex](x), so P [itex]\in[/itex] P.
This seems like a paradox to me, so all I have to prove is that a set can't contain itself. But how? I've got a gut feeling it's closely related with Russels paradox, but I can't get it.