Restriction is a notion with etymological origin in restrictive Latin. It's about the process and consequence of restricting. This verb, for its part, refers to limiting, adjusting, narrowing or circumscribing something.
For example: "The government announced a restriction on the import of chemical products with the aim of promoting national production" , "This literary contest does not set any restriction on the extent of the work" , "The organizers of the congress will establish a time restriction so that the speakers do not overdo their presentations ” .
It is common for the authorities to establish restrictions on the purchase of certain products when there is a shortage situation. The aim is to prevent the products in question from being out of stock and no longer available.
Suppose that, for different reasons, the amount of milk that is for sale in a country is low. To prevent hoarding by some, which would lead to a shortage for others, the government establishes a purchase restriction: each person can only buy three liters of milk a week. This measure seeks to distribute the available stock equitably.
The restriction, in general, always marks a limit. A young person who has to take an exam to enter a university is given a maximum period of two hours to complete it. This means that there is a restriction to complete the exam: the applicant cannot take more than two hours to take the test. If you do not comply with the restriction, your evaluation is not accepted.
In the field of mathematics, it is called a restriction from one function to another that is defined in a subset of the domain of the initial (the domain is, for its part, a set that gathers the values for which a function is defined), and that it does not cause a change with respect to the values assigned to each element. It is correct to say that the function to which this restriction is applied is an extension of the resultant.
Let's see below an example of this concept: if we have a set of people of all ages and another of titles of movies that have been released in the last ten years, and a function relates them by graphing which is the favorite title of each person, we can apply a restriction that only takes into account individuals whose age group is between 30 and 40 years old, to focus on the tastes of that generation; This gaze has limits at both ends, since it ignores people younger than 30 and older than 40, so the initial function can be considered an extension of it, because it shows a greater number of relationships (in fact, it shows them all).
As has been seen so far, it is necessary to reduce the domain of a function to obtain one of its possible reductions. On the contrary, the term extension can also be used to speak of a function that contemplates a more numerous domain, although always with the condition of not varying the images of the first (also called range or value field , the image is the set of the values that a given function can take).