- empty product
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The result of multiplying no numbers (defined in order to be able to extend certain mathematical concepts, such as the product of n numbers, to the case where n = 0).
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empty product
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Empty product — In mathematics, an empty product, or nullary product, is the result of multiplying no factors. It is equal to the multiplicative identity 1, given that it exists for the multiplication operation in question, just as the empty sum the result of… … Wikipedia
Empty sum — Not to be confused with Zero sum. In mathematics, an empty sum, or nullary sum, is a summation involving no terms at all. The value of any empty sum of numbers is conventionally taken to be zero. For summations defined in terms of addition of… … Wikipedia
Empty set — ∅ redirects here. For similar looking symbols, see Ø (disambiguation). The empty set is the set containing no elements. In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality… … Wikipedia
Product (category theory) — In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the cartesian product of sets, the direct product of groups, the direct… … Wikipedia
Product (mathematics) — In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied. The order in which real or complex numbers are multiplied has no bearing on the product; this is known as the commutative law of… … Wikipedia
Product topology — In topology and related areas of mathematics, a product space is the cartesian product of a family of topological spaces equipped with a natural topology called the product topology. This topology differs from another, perhaps more obvious,… … Wikipedia
Empty function — In mathematics, an empty function is a function whose domain is the empty set. For each set A , there is exactly one such empty function :f A: varnothing ightarrow A.The graph of an empty function is a subset of the Cartesian product empty;… … Wikipedia
Empty vessel — The phrase empty vessel literally means a container with nothing inside. It has additional significance in various areas.In literatureThe quotation, As empty vessels make the loudest sound, so they that have the least wit are the greatest… … Wikipedia
Cartesian product — Cartesian square redirects here. For Cartesian squares in category theory, see Cartesian square (category theory). In mathematics, a Cartesian product (or product set) is a construction to build a new set out of a number of given sets. Each… … Wikipedia
Wick product — In probability theory, the Wick product:langle X 1,dots,X k angle,named after physicist Gian Carlo Wick, is a sort of product of the random variables, X 1, ..., X k , defined recursively as follows::langle angle = 1,(i.e. the empty product… … Wikipedia
