Hi Folks: As an amateur, I am trying to prove there is no set that contains all sets without using Russell's paradox. My argument is as follows: Suppose arbitrary set S contains S. If S contains set X such that X not= S, Then S - S not= { }. But this is a contradiction; hence if S contains S, then S contains only S. Thus |S| = 1 (cardinality = 1) and so S cannot contain all sets.
Is this argument logically valid?
Thank you.
Rich B. (note: I am not a student; this is not homework)
Is this argument logically valid?
Thank you.
Rich B. (note: I am not a student; this is not homework)