Multiplicity (mathematics)
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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".
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See also
- Zero (complex analysis)
- Set (mathematics)
- Fundamental theorem of algebra
- Fundamental theorem of arithmetic
- Algebraic multiplicity and geometric multiplicity of an eigenvalue
- Frequency (statistics)
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