English edit

Etymology edit

factor +‎ -ial

Pronunciation edit

  • IPA(key): /fækˈtɔːɹi.əl/
    • (file)

Noun edit

factorial (plural factorials)

  1. (mathematics, combinatorics) 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.
    • 1916 July, M. Mott-Smith, “The Arithmetical Pyramid of Many Dimensions”, in The Monist, volume 26, number 3, →DOI, page 428:
      The expression   means the number of combinations of   things taken   at a time. It is also written  , and is equal to
       
      or  , in which   is read "factorial  " and denotes the product of all the integral numbers from   to   inclusive.
    • 2018 September, Colin Foster, “What is the formula for factorial?”, in Mathematics in School[1], volume 47, number 4, page 40:
      This playing around with consecutive integers reminded one of the students of factorials, and he asked about products of integers, which I said could be expressed similarly as
       
      But what does this equal?
      Well, of course we can say that it is equal to   factorial and write
       
      and then use our calculators, but inventing a new symbol like 'factorial' feels like an admission of defeat!

Usage notes edit

"n!" is read as "factorial of n" or "n factorial."

Hyponyms edit

Related terms edit

Translations edit

Adjective edit

factorial (comparative more factorial, superlative most factorial)

  1. (mathematics) Of or pertaining to a factor or factorial.
    • 1903, Arthur Schuster, “On some Definite Integrals, and a New Method of Reducing a Function of Spherical Co-ordintes to a Series of Spherical Harmonics”, in Philosophical Transactions of the Royal Society A, volume 200, →DOI, →JSTOR, page 182:
      I shall denote, as usual, the factorial product of the numbers up to   by  , but I have found it necessary to introduce a separate notation for the products of successive even or odd numbers. I consequently define
       
      Starting with
       
      it follows that, for positive values of  ,
       
      where the last factor is either   or  , according as   is odd or even.
    • 1995, K. E. Hirst, Numbers, Sequences and Series, Butterworth-Heinemann, →ISBN, page 21:
      The definition of addition is an example of definition by induction, sometimes called recursive definition. As another example of this, consider the following inductive definition of the factorial function.
      We define   for   by the following two properties,
      (i)   is defined to be  ,
      (ii) for all  , we define   to be  .
  2. Of or pertaining to a factor, a kind of business agent.
    • 2004, The Digest: Annotated British, Commonwealth, and European Cases:
      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. (dated) Of or pertaining to a factory.

Derived terms edit

See also edit

References edit

Further reading edit

Portuguese edit

Noun edit

factorial m (plural factoriais)

  1. Pre-reform spelling (until Brazil 1943/Portugal 1990) of fatorial. Still used in countries where the agreement hasn't come into effect; may occur as a sporadic misspelling.

Adjective edit

factorial m or f (plural factoriais)

  1. Pre-reform spelling (until Brazil 1943/Portugal 1990) of fatorial. Still used in countries where the agreement hasn't come into effect; may occur as a sporadic misspelling.

Romanian edit

Etymology edit

Borrowed from French factorielle.

Adjective edit

factorial m or n (feminine singular factorială, masculine plural factoriali, feminine and neuter plural factoriale)

  1. factorial

Declension edit

Spanish edit

Pronunciation edit

  • IPA(key): /faɡtoˈɾjal/ [faɣ̞.t̪oˈɾjal]
  • Rhymes: -al
  • Syllabification: fac‧to‧rial

Adjective edit

factorial m or f (masculine and feminine plural factoriales)

  1. factorial

Derived terms edit

Noun edit

factorial m (plural factoriales)

  1. (mathematics) factorial

Further reading edit