These can be represented on a number line. Therefore, numbers like -5, -6/2, 0, 1, 2 or 3.5 are considered real because they express a successive numerical representation on an imaginary line. The capital letter R is the symbol that represents the set of real numbers.
These are a set of numbers and between them there are several subgroups. Thus, 6/3 is a rational number because it expresses the fraction of something, in turn, it is a real number because it does not fail to indicate a number line. If we take the number 4 as a reference, we will be facing a natural number, which is part of the real numbers.
Following the example of the number 4, it is not just a natural number, but a positive integer and, at the same time, a rational number (4 is the result of the fraction 4/1). All this without ceasing to be a real number.
In the case of the square root of 9, we are also faced with a real number through the result of 3, that is, a positive integer that is at the same time rational and that can be expressed in the form 3/1.
In mathematical terms, these can be classified as follows. In the first place may include the set of natural numbers , N represented by uppercase letters (that is 1, 2, 3, 4, etc.), as well as the prime and composite numbers, as both are also natural.
On the other hand, we have the integers represented by the capital letter Z, which in turn are divided into: positive integers, negative integers and 0. In this way, both natural and integer numbers are encompassed within the set of rational numbers represented by the capital letter Q.
In relation to the irrational numbers, the same are usually represented by the letter I capital and meet the following characteristics: they can not be represented in fraction form and have decimal numbers Ds on a periodic basis, for example, PI or golden number (these numbers they are also real numbers, as they express an imaginary line).
Finally, the set of rational and irrational numbers forms, in turn, the total set of such numbers.