Multiplicity (mathematics) | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-10-07

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Multiplicity_(mathematics)


00:00:01 1 Multiplicity of a prime factor
00:00:02 2 Multiplicity of a root of a polynomial
00:00:04 2.1 Behavior of a polynomial function near a multiple root
00:00:05 3 Intersection multiplicity
00:00:06 4 In complex analysis
00:00:08 5 References
00:00:10 Intersection multiplicity
00:00:12 In complex analysis
00:00:14 1, the root is called a simple root.We can also define the multiplicity of the zeroes and poles of a meromorphic function thus: If we have a meromorphic function f



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SUMMARY
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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 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".