- #1
nikkor180
- 13
- 1
Greetings: I am attempting to prove that no set contains all sets without Russell's paradox. What I have thus far is this:
Let S be an arbitrary set and suppose S contains S. If X is in S for some X not=S, then S - S cannot be empty. But this is a contradiction; hence if S contains S, then S contains only S. Thus S cannot contain all sets.
Is this argument valid?
Thank you.
Rich B. (note: I am not a student; this is not homework)
Let S be an arbitrary set and suppose S contains S. If X is in S for some X not=S, then S - S cannot be empty. But this is a contradiction; hence if S contains S, then S contains only S. Thus S cannot contain all sets.
Is this argument valid?
Thank you.
Rich B. (note: I am not a student; this is not homework)