# Russell’s Paradox

If a set can contain sets as elements, can it contain itself?

Let $S={X∣¬(X∈X)}$. Is $S∈S$?

We can prove that this premise is false, as we saw in SE212 (just search SE212 (just search Russell’s Paradox).

If a set can contain sets as elements, can it contain itself?

Let $S={X∣¬(X∈X)}$. Is $S∈S$?

We can prove that this premise is false, as we saw in SE212 (just search SE212 (just search Russell’s Paradox).