Multiplicity (mathematics)
![Graph of the polynomial p(x) = x3 + 2x2 − 7x + 4 with its roots (zeros) -4 and 1. The root -4 is a 'simple' root (of multiplicity 1), and therefore the graph crosses the x-axis at this root. The root 1 is of even multiplicity and therefore the graph bounces off the x-axis at this root.](/Images/godic/202501/09/Polynomial_roots_multiplicity.svg2256.png")
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 multiplicity".