Multiplicity (mathematics)

（重定向自Multiple root）

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.

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".

单词	Multiple root
释义	Multiple root 原声例句 Osmosis-神经 If it bulges out towards the center of the spinal cord, it could compress multiple nerve roots on both sides, or laterally, compressing one nerve root on one side. 如果它是向脊髓中心突出，则可能压迫两侧的多个神经根或仅压迫一侧的单一神经根。英语百科 Multiplicity (mathematics) （重定向自Multiple root） 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".
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