The empty set is the set which has no members.

Symbols for the empty set are usually either "{}" or "Φ" (the greek letter "phi").

Note that zero (0) and the empty set (Φ) do NOT represent the same thing.

Set A has four members, set B has an infinite number of members, set C has one member and set D (the empty set) has zero members.

Let set E represent the set of all triangles that have five sides.

Since there are no triangles with five sides (triangles must have exactly three sides), set E is best represented by the empty set.

E = Φ

Let set H represent the intersection of sets A and B (H = A ∩ B).

In other words let set H contain all members common to sets A and B.

Since there are no members H = Φ, or A ∩ B = Φ