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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.
Second, and empty product is not the result of anything, it is something like "0!" whose value is 1, but it is not identical to 1 (or otherwise conversely "1 is an empty product", which seems a bad formulation). In short, one should make distinction between expressions and there values, and an empty product is an expression.
Notion hosts its own template gallery, where users can browse through templates made by other Notion creators. However, not all of these templates are free to use. Some creators profit from selling Notion templates. Jason Ruiyi Chen, from Singapore, made $239,000 by selling his Notion templates to his Twitter audience.
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An Amazon.com exclusive is a product, that is available exclusively on Amazon.com. Some DVDs are produced by the owner of the film or product, while others are produced by Amazon.com itself. The DVDs produced by Amazon are made using its "CreateSpace" program, in which DVDs are created, upon ordering, using DVD-R technology.
As a result, the empty set is the unique initial object of the category of sets and functions. The empty set can be turned into a topological space, called the empty space, in just one way: by defining the empty set to be open. This empty topological space is the unique initial object in the category of topological spaces with continuous maps.
In mathematics, an empty sum, or nullary sum, [1] is a summation where the number of terms is zero. The natural way to extend non-empty sums [ 2 ] is to let the empty sum be the additive identity . Let a 1 {\displaystyle a_{1}} , a 2 {\displaystyle a_{2}} , a 3 {\displaystyle a_{3}} , ... be a sequence of numbers, and let