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.
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