 What sets are there? The simplest collections are given by enumeration (the set {Tom, Dick, Harry} of men I see over there, or (more abstractly) the set \(\{-2, 2\}\) of square roots of 4. But even for finite sets it is often more convenient to give a defining property for elements of the set: consider the set of all grandmothers who have a legal address in Boise, Idaho; this is a finite collection but it is inconvenient to list its members. The general idea is that for any property \(P\), there is a set of all objects with property \(P\). This can be formalized as follows: For any formula \(P(x)\), there is a set \(A\) (the variable \(A\) should not be free in \(P(x))\) such that