What is "empty product"

n. (context arithmetic English) The result of multiplying no numbers, conventionally defined to equal one.

In mathematics, an empty product, or nullary product, is the result of multiplying no factors. It is by convention equal to the multiplicative identity 1 (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.

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; these are discussed below.