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 equation has a root at a given point.
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 (sometimes implicit) 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".
Read more about Multiplicity (mathematics): Multiplicity of A Prime Factor, Multiplicity of A Root of A Polynomial, In Complex Analysis
Famous quotes containing the word multiplicity:
“Is a Bill of Rights a security for [religious liberty]? If there were but one sect in America, a Bill of Rights would be a small protection for liberty.... Freedom derives from a multiplicity of sects, which pervade America, and which is the best and only security for religious liberty in any society. For where there is such a variety of sects, there cannot be a majority of any one sect to oppress and persecute the rest.”
—James Madison (1751–1836)