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correspondence

To better understand, here is a definition of correspondence :
Given two sets A and B, there is a correspondence between them when a function every element of A has an image in B, and every element of B has a controimmagine in A.


So two together can be put into correspondence only when they have the same number of elements (cardinality).

Usually a report is a set of pairs generated by a proposition open to two variables p (x, y) becomes a function when each element of first set is present in at least a couple becomes a bijection when every element of the first or second set is present in only a couple.

Here's an example:
A = {A, B, C, D}
B = {1, 2, 3, 4, 5} With the following function
injection (one correspondence):

And the following bijective function (correspondence):

analysis of the two functions in the images we deduce that:

1. In the first match is unique and the function is injective, because the domain of the function corresponds to all A same and every element x of A has a distinct image in B.
2. The second correspondence is bijective and the function is bijective, since even the codomain corresponds to B and each element has associated with a single line item in the collection.

Here are some examples :

1. The binary alphabet is B = {0, 1}, and a signal to be interpreted by the CPU or any electronic circuit, must be translated into an electrical signal with voltage, such as the voltage of 0 corresponds to the binary 0, 1 and 5 is the voltage rail. We have created a correspondence between the binary alphabet B = {0, 1} and the set of voltages Circuit considered V {0, 5}.
2. A bijective function more complex can form between two classes of a school, 1B and 2C. 1B = {Mark, John, Michael, Lorenzo, Angela, Vanessa, Isabella and 2C} {Mary, Francis, Anna, Frances, Joseph, Simon, Luca}, a relation R: A → B given by p (x, y) "x is of the same sex y ' with x ∈ A and y ∈ B. R can be considered as a bijective function, it examined the set of pairs is obtained, analyzed the domain, codomain, and correspondence that you create.
3. between two cars (Fiat Punto and Volkswagen Golf), if we consider the set of standard parts the first and second (ie every car should have. For example: front left wheel, front right, rear left, etc. ...), we can make a correspondence between the sets as each car has to have those pieces. But if we consider the total set of pieces of each car, we will not have a correspondence, and perhaps even a function.

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