Expert: Josh - 1/28/2005

Question
What is empty set? I have looked up resources for definition but could not quite coprehend their intricate explanations. Thank you for your time.

Ang-sui

Answer
Put simply, an empty set is a set which contains no element. It is usually represented with the Greek symbol "Phi" (which looks like drawing a bar "/" through a circle).

Consider the following example.
Let A be the set of positive integers, i.e., A={1,2,3...}.
Let B be the corresponding set of numbers, constructed by adding an offset of 0.5 to A.
i.e., B={1.5,2.5,3.5,...}.

Now, in set notations, the vertical bar is translated as "given that" in the following description.

Mathematically, A={n | n is an element of Z} and
B={n+0.5 | n is an element of Z}

If we take the intersection between the two sets, A and B, this yields an empty set, since they have nothing in common. So, A and B = Phi, where Phi represents the empty set {}.