Russell’s paradox states that the RussellianClass𝑅 defined by
(∀𝔐𝑥)[𝑥∈𝑅⟺𝑥∉𝑥]
is not a set. set
For if it were a set, either 𝑅∈𝑅 or 𝑅∉𝑅 implies its opposite, which is absurd.
The main issue at hand is unrestricted comprehension,
and different approaches to axiomatic set theory must take care to resolve this paradox.