The word multiplicity is a general term meaning "the number of values for which a given condition holds." For example, the term is used to refer to the value of the totient valence function or the number of times a given polynomial equation has a root at a given point.
Let be a root of a function , and let be the least positive integer such that . Then the power series of about begins with the th term,
and is said to have a root of multiplicity (or "order") . If , the root is called a simple root (Krantz 1999, p. 70).