Empty product

Common card · No. 437908

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; when numbers are implied, it becomes one), just as the empty sum — the result of adding no numbers — is by convention equal to the additive identity (zero). 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.

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