Set: Definition

A collection of well-defined objects is called a SET. Each object inside a set is called its ELEMENT or MEMBER. By convention, sets are denoted using capital letters — A, B, C, and so on — while the elements of a set are denoted using small letters — a, b, c, x, y, z, and so on. If x is an element of a set A, we write $x \in A$, read as 'x belongs to A'. If x is NOT an element of A, we write $x \notin A$, read as 'x does not belong to A'. For example, zero is a whole number but not a natural number in this book's convention (natural numbers start at 1). So we write $0 \in W$ (where W is the set of whole numbers, $W=\{0,1,2,3,\ldots\}$) but $0 \notin N$ (where N is the set of natural numbers, $N=\{1,2,3,\ldots\}$). This N-versus-W distinction — whe …