Null or Empty Set

The empty set, or null set denoted by $\emptyset$ or by {} is the set which contains no elements. For example $\{x \enskip \vert \enskip x \in \Nat$ and $2x = 1\} = \emptyset$. As a further example, if $A = \{1,2,4\}$ and $B = \{3,5,9,10\}$ then $A \cap B = \emptyset$ (A and B have no elements in common).

Note that for any given set A, then $\emptyset \subseteq A$, that is the empty set is a subset of any set A. Furthermore, if $A \subseteq B$, $A \not= \emptyset$ and $A \not= B$, then A is called a proper subset of B. It is important to remember that we use ``$\subset$'' to denote a proper subset and ``$\subseteq$'' for the more general subset relation.

A word of caution here - do not confuse the empty set $\emptyset$with the set $\{0\}$ which denotes the non-empty set consisting of the single element zero.