One relatively simple but informal description of the problem is that the statement is self-referencing. Related is the Bertrand Russell paradox: X = {z | z i

One relatively simple but informal description of the problem is that the statement is self-referencing. Related is the Bertrand Russell paradox: X = {z | z is not an element of z} So, X is an element of X if and only if it is not -- a contradiction. The usual solution was to have two steps: (1) Over here, say, on the left, we have everything we want to regard as elements. (2) On the right, we have everything we want to regard as sets. The sets consist only of elements. That's a good fix. For more, there is the elegant, long popular, P. Halmos Naive Set Theory, now available in PDF, LaTeX, etc. For more there is the appendix to J. Kelley, General Topology. For more there is P. Suppes, Axiomatic Set Theory. For more, sure you want more????