Editing Russell's paradox (section)

== Informal presentation ==
Most sets commonly encountered are not members of themselves. Let us call a set "normal" if it is not a member of itself, and "abnormal" if it is a member of itself. Clearly every set must be either normal or abnormal. For example, consider the set of all [[square]]s in a [[plane (geometry)|plane]]. This set is not itself a square in the plane, thus it is not a member of itself and is therefore normal. In contrast, the complementary set that contains everything which is '''not''' a square in the plane is itself not a square in the plane, and so it is one of its own members and is therefore abnormal.

Now we consider the set of all normal sets, ''R'', and try to determine whether ''R'' is normal or abnormal. If ''R'' were normal, it would be contained in the set of all normal sets (itself), and therefore be abnormal; on the other hand if ''R'' were abnormal, it would not be contained in the set of all normal sets (itself), and therefore be normal. This leads to the conclusion that ''R'' is neither normal nor abnormal: Russell's paradox.