# Math Help - Set of all sets paradox

1. ## Set of all sets paradox

Let R = {X : X is a set and X is not an element of X }. Is the statement R is an element of R true or false?

Thanks for all the help!

2. Originally Posted by jstarks44444
Let R = {X : X is a set and X is not an element of X }. Is the statement R is an element of R true or false?
If $R\in R$ then $R\notin R$.
If $R\notin R$ then $R\in R$.
What do you think?

3. I think I just pooped my pants!
But seriously...
j, you basically have the answer already (even before considering Plato's explicit argument) that this is a paradox. If this is part of an assignment, you should elaborate a bit on the above reasoning (R in R --> R not in R, etc) and maybe add some "original" commentary.

4. (sighs) I need a shave....

-Dan

(Sorry, I just couldn't resist that one.)