And the idea in the context of the original post is that this is supposed to be a parody of a formal math definition in a paper or textbook (using Jabberwocky vocabulary instead of real math vocabulary).
No, the point was that πβπ is a typo and πβπ is what was intended. Type theory will reject the mistake but set theory will accept it. This is then presented as a reason why mathematicians should prefer type-theory-based proof assistants to set-theory-based ones, since the former will catch these kinds of mistakes while the later won't.
Thatβs possible. For instance, X = {{}} and U = {}. Or in general, if X_0 = {} and X_{i+1} = {X_0, ..., X_i}, then X_i is both an element and a subset of X_j whenever i < j.