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Cartesian product

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Before entering fully into the establishment of the Cartesian product meaning, it is necessary that we proceed to determine the etymological origin of the two words that shape it:
-Product derives from Latin, from "productus", which is equivalent to "produced" and which is the result of the sum of the prefix "pro-", synonymous with "forward", and the adjective "ductus", which can be translated as "guided".
-Cartesian, meanwhile, of "Cartesius" which was the Latin name of the French philosopher René Descartes, who was the one who shaped Cartesianism or Cartesian dualism. This doctrine or ideology came to establish, among many other things, that the human being was composed of two substances: the extensive and the thinking.

The notion of Cartesian product it is used in the field of math , more precisely in the field of algebra . The Cartesian product reveals a order relationship between two sets , becoming a third set.

The Cartesian product of a set TO and of a set B it is the set constituted by the all ordered pairs that have a first component in TO and a second component in B .

Let's see a example . If the whole TO It is formed by the elements 3 , 5 , 7 and 9 while the whole B houses the elements m and r , the Cartesian product of both sets is as follows:

A x B = {(3, m), (3, r), (5, m), (5, r), (7, m), (7, r), (9, r), (9, r)}

The Cartesian product, therefore, is made up of all ordered pairs that can be formed from two certain sets . Each ordered pair consists of two elements: the first element belongs to one set and the second element to the other. If we continue with our example, in the ordered pair (3, m) , 3 It is the first element (corresponds to the set TO ) and m it is the second element (belonging to the set B ).

It is important to establish, in addition to all of the above, that when we talk about Cartesian products we have to refer to two possible cases or types of generalizations. Thus, on the one hand, there is the so-called finite case, which is one that starts from a finite number of sets (A1, A2, A3… An). The same Cartesian product would be the group of numbered lists whose element is in A1, the second in A2 ...

The infinite case would be one in which, starting from a large family of sets with all the infinite probability and of an arbitrary nature, when defining the relevant Cartesian product, what is the definition of the aforementioned numbered lists would be substituted.

Suppose, in one house, there are three people (Charles, Juan and Antonia) and two books (Hopscotch and One hundred years of loneliness). The Cartesian product of both sets (people and books ) will consist of all possible distributions of literary works among individuals.

P x L = {(Carlos, Rayuela), (Carlos, One Hundred Years of Solitude), (Juan, Rayuela), (Juan, One Hundred Years of Solitude), (Antonia, Rayuela), (Antonia, One Hundred Years of Solitude)}
Bliss information It can be useful to create an organization chart that specifies how the two books will be distributed so that everyone has the opportunity to read them at some point.

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