What is an integer?

In mathematical theory and tasks, oftenthere is such a thing as an "integer". Often, on the basis of this concept, a solution of the problem is constructed, or a proof of a certain statement. If the student does not know what an integer is, he may not understand the essence of the proof, or he will not solve the problem.

In fact, any number can be called an integer,which does not have a fractional part. Thus, the numbers 3, 8, 456, -12, 0, -500 will be integers. Unlike them, numbers like 3.5 or 3? You can not call them whole because they have a fractional part.

If you ask for help in defining the concept"An integer" to a mathematical theory, we get the following statement: "An integer is a number that can be obtained as a result of subtraction and addition of natural numbers." Recall that natural numbers are those that we use when counting: 1, 2, 3 and so on.

This statement can be very easily verified. For example, to get 5, you need to add 2 and 3. To get -5, we need to subtract 10 from 5.

Often people, after learning what a "prime number" is, are interested in whether the number is prime. If the first rule specified in the article is followed, the number 0 is simple, since it does not have a fractional part.

Also confirms this and the second rule: to get the number 0 it is possible, if you subtract from the natural number of it, that is, subtract 2 from 2, 3 of 3 and so on.

Solving mathematical problems, pay attention to the condition: if it is indicated that a certain number is an integer, then this, essentially, can affect the solution.