# Set of all sets paradox

• Mar 10th 2011, 12:55 PM
jstarks44444
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!
• Mar 10th 2011, 01:06 PM
Plato
Quote:

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 $\displaystyle R\in R$ then $\displaystyle R\notin R$.
If $\displaystyle R\notin R$ then $\displaystyle R\in R$.
What do you think?
• Mar 10th 2011, 01:11 PM
TheChaz
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.
• Mar 10th 2011, 01:43 PM
topsquark
(sighs) I need a shave....

-Dan

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