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In [[mathematics]], an '''empty product''', or '''nullary product''', is the result of [[multiplication|multiplying]] no numbers. Its numerical value is [[1 (number)|1]] (the [[multiplicative identity]]), just as the [[empty sum]] — the [[sum]] of no numbers — is [[0 (number)|zero]] (the [[additive identity]]). This fact is used in [[discrete mathematics]], [[elementary algebra|algebra]], the study of [[power series]], and [[programming|computer programs]].
The term "empty product" is most often used in the above sense when discussing [[arithmetic]] operations. However, the term is sometimes employed when discussing the value of 0<sup>0</sup>, set-theoretic intersections, categorical products, and products in computer programming; these are discussed below.
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