>According to naive set theory, any definable collection is a set. Let R be the set of all sets that are not members of themselves. If R is not a member of itself, then its definition dictates that it must contain itself, and if it contains itself, then it contradicts its own definition as the set of all sets that are not members of themselves.

R in R => R not in R
and
R not in R => R in R
implies
R in R <=> R not in R

Therefore R is not in R and not not in R. It is a contradiction for R to exist.

Ok, now ill go.
def R' as an empty set

now add in a set which does not contain itself, unless that set is R or R' itself

do it infinity times

Now R is a set which contains every set which does not contain itself, excluding R

We can choose to stop counting because from this point we can add or not add R as we please forever and ever.

Just happy we got all the other sets and can just put r in if i feel like it because it doesnt really matter in the grand scheme of things.

iterative construction, feels good man, got all of em and can just stop worrying about the paradoxical one. fuck phillosophy n shit man

QED