factorial

名词 n. 形容词 adj.
中文释义

英文释义

名词 n.
  1. The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 × 2 × 3 × 4 × 5 = 120.
    — The expression #123;#125;#95;nC#95;r means the number of combinations of n things taken r at a time. It is also written #92;binomnr, and is equal to#92;frac#123;n(n-1)(n-2)(n-3)#92;cdots#92;cdots(n-r#43;1)#125;#123;r#33;#125;or n#33;#47;r#33;(n-r)#33;, in which r#33; is read "factorial r" and denotes the product of all the integral numbers from 1 to r inclusive.
形容词 adj.
  1. Of or pertaining to a factor or factorial.
    — I shall denote, as usual, the factorial product of the numbers up to n by n#33;, but I have found it necessary to introduce a separate notation for the products of successive even or odd numbers. I consequently definen#33;#33;#61;n#92;cdot(n-2)#33;#33;.Starting with1#33;#33;#61;1,#92;quad 2#33;#33;#61;2,it follows that, for positive values of n,n#33;#33;#61;n#92;cdotn-2#92;cdotn-4#92;cdots,where the last factor is either 1 or 2, according as n is odd or even.
  2. Of or pertaining to a factor, a kind of business agent.
    — The latter sold the goods to a customer who was cashier to certain creditors of the agents without disclosing the factorial capacity in which they acted.
  3. Of or pertaining to a factory. dated

词形变化

factorials plural more factorial comparative most factorial superlative

词汇关系

衍生词
bifactorial factorial experiment factoriality factorialization factorialize factorially factorial table hyperfactorial interfactorial monofactorial multifactorial nonfactorial plurifactorial polyfactorial semifactorial subfactorial superfactorial trifactorial unifactorial
相关词
primorial

词源

词源 1
Etymology tree
English factor
Proto-Indo-European *h₂el-der.?
Proto-Italic *-ālis
Latin -ālisder.
Old French -ialder.
Middle English -ial
English -ial
English factorial
From factor + -ial.
词源 2
Etymology tree
English factor
Proto-Indo-European *h₂el-der.?
Proto-Italic *-ālis
Latin -ālisder.
Old French -ialder.
Middle English -ial
English -ial
English factorial
From factor + -ial.
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