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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), just as the empty sum—the result of adding no numbers—is by convention zero, or the additive identity.
Since the empty category is vacuously a discrete category, a terminal object can be thought of as an empty product (a product is indeed the limit of the discrete diagram {X i}, in general). Dually, an initial object is a colimit of the empty diagram 0 → C and can be thought of as an empty coproduct or categorical sum.
The empty product on numbers and most algebraic structures has the value of 1 (the identity element of multiplication), just like the empty sum has the value of 0 (the identity element of addition). However, the concept of the empty product is more general, and requires special treatment in logic, set theory, computer programming and category ...
You can still define repeated products, but now there's nothing to assign to the empty product. If you don't specify what the empty product means (that is, give a convention), then it simply has no meaning, notwithstanding there's a best choice for the meaning to give it. --Trovatore 01:41, 28 September 2019 (UTC)
The distinction between real prices and ideal prices is a distinction between actual prices paid for products, services, assets and labour (the net amount of money that actually changes hands), and computed prices which are not actually charged or paid in market trade, although they may facilitate trade. [1]
0 (zero) is a number representing an empty quantity.Adding (or subtracting) 0 to any number leaves that number unchanged; in mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures.
Empty wallet season hits different when you know where to look for affordable wins. These 20 budget-friendly champions prove that dropping serious cash isn't always the answer to upgrading your life.
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 or rings, and the product of topological spaces.