# Multiplicity (mathematics)

In mathematics, the **multiplicity** of a member of a multiset is the number of times it appears in the multiset. For example, the number of times a given polynomial has a root at a given point is the multiplicity of that root.

The notion of multiplicity is important to be able to count correctly without specifying exceptions (for example, *double roots* counted twice). Hence the expression, "counted with multiplicity".

If multiplicity is ignored, this may be emphasized by counting the number of **distinct** elements, as in "the number of distinct roots". However, whenever a set (as opposed to multiset) is formed, multiplicity is automatically ignored, without requiring use of the term "distinct".