Empty product

For the non-empty product that equals to zero, see zero-product property.

In mathematics, an empty product, or nullary product or vacuous product, is the result of multiplying no factors. It is by convention equal to the multiplicative identity (assuming there is an identity for the multiplication operation in question), just as the empty sum—the result of adding no numbers—is by convention zero, or the additive identity.[1][2][3][4] When numbers are implied, the empty product becomes one.

The term empty product is most often used in the above sense when discussing arithmetic operations. However, the term is sometimes employed when discussing set-theoretic intersections, categorical products, and products in computer programming.

  1. ^ Jaroslav Nešetřil, Jiří Matoušek (1998). Invitation to Discrete Mathematics. Oxford University Press. p. 12. ISBN 0-19-850207-9.
  2. ^ A.E. Ingham and R C Vaughan (1990). The Distribution of Prime Numbers. Cambridge University Press. p. 1. ISBN 0-521-39789-8.
  3. ^ Lang, Serge (2002), Algebra, Graduate Texts in Mathematics, vol. 211 (Revised third ed.), New York: Springer-Verlag, p. 9, ISBN 978-0-387-95385-4, MR 1878556, Zbl 0984.00001
  4. ^ David M. Bloom (1979). Linear Algebra and Geometry. CUP Archive. pp. 45. ISBN 0521293243.