Slightly Elevated Glucose Level 6.4

injective function, surjective and bijective.

First start by saying that bijective you write, but bijective (with both).

functions are relationships that we know how to generate a unique correspondence between two sets, as each element of the first set has associated only one element in the second, but is not necessarily true the incontrario. A function-type relationship between two sets A and B then gives birth to a correspondence. Matches can be of various types:

one to many :

Each element x of A can have multiple images in B y



many to one : Each element y of B can have more controimmagini x in A

one by one
• : Each element x of A has only one image in B and y is the opposite.
many to many
• : Each element x of A can have multiple images in B y and the latter have more Possoni controimmagini x in A. According to correspondence which generates a function, we can say that the property meets one of the following:
• A function is said surjective when the codomain is the set B, then every element in B has a controimmagine A. A function is said
injective when
• distinct elements of A, have distinct images in B, then each element can be associated with only one other element that has not been associated with another. A function is said is surjective and bijective when injected simultaneously. So all the elements of A have distinct images in B and all elements of B are distinct in controimmagini A. Then is injective, surjective, but also because nothing remains inassociato.

A function is injective or bijective correspondence-type "one", while a surjective can be of various types.

Examples of functions:
• 1) In a team of players, each player has a number that identifies it on the football field. So we have all of the players A, B and all the natural numbers from 1 to 30. For each player must match to force a number, so it's a function because every element of A should have an image in B. Then we know that a player only has an associated ID number different from the other players, then the function is injective because the correspondence is one to one. If a team reaches the maximum number of players, in our case 30, the function becomes surjective, since each number is a different player. The function being injective and surjective, it becomes bijective. 2) We have the set A that contains all types of cars in Italy and the set T contains all the license plates as possible. Given a set I contains all the cars registered, and a relation R which associates each element x of the one discrete element y of T, we can say that R is a function because each car must have a registered license plate. Then we know that every registered car number plate is one distinct from others, then the function is injective. And finally, though we know that not all the plates of all T are associated with the whole car, then the function is not surjective, and even bijective.