definition of real numbers

Real numbers are all those that can be represented on a number line, Therefore, numbers like -5, - 6/2, 0, 1, 2 or 3.5 are considered real because they can be reflected in a successive numerical representation, in a imaginary line. The capital letter R is the symbol that represents the set of real numbers.

Examples of real numbers

Real numbers are a set of numbers and between them there are several subgroups. Thus, - 6/3 is a rational number because it expresses a portion of something and, in turn, it is a real number because it can be indicated on a number line. If we take the number 4 as a reference, we are facing a natural number, which is also part of the real numbers.

Continuing with the example of the number 4, it is not only a natural number, but it is also a positive integer and at the same time a rational number (4 is the result of the fraction 4/1) and all this without ceasing to be a number real.

In the case of the square root of 9, we are also dealing with a real number, since the result is 3, that is, a positive integer that at the same time is rational, since it can be expressed in its 3/1 form.

A classification of real numbers

In mathematical terms, real numbers can be classified as follows. In the first section we could include the set of natural numbers, represented by a capital N and which are 1, 2, 3, 4, etc., as well as prime and composite numbers, since both are equally natural.

On the other hand, we have the integers represented by a capital Z and which in turn are divided into positive integers, negative integers and 0. In this way, both natural numbers and integers are encompassed within the set of rational numbers represented by the capital letter Q.

As for irrational numbers, which are normally represented by the letters ll, they are those that meet two characteristics: they cannot be represented as a fraction and they have infinitive decimal numbers periodically, for example the number pi or the golden number ( these numbers are also real numbers, since they can be captured on an imaginary line).

In conclusion, the set of rational numbers and the set of irrationals in turn make up the total set of real numbers.

Photos: iStock - asterix0597 / Kenan Olgun

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