A **number** is the expression of a **quantity** in relation to its **unity** . The term comes from Latin *numĕrus* and refers to a **sign** or a **set of signs** . The theory of numbers groups these signs into different groups. The **natural numbers** , for example, include one (1), two (2), three (3), four (4), five (5), six (6), seven (7), eight (8), nine (9) and usually at zero (0).

The concept of **real numbers** arose from the use of common fractions by the Egyptians, close to the year **1,000 BC** . The development of the notion continued with the contributions of the Greeks, who proclaimed the existence of irrational numbers.

The real numbers are those that can be expressed by a **whole number** (3, 28, 1568) or **decimal** (4.28; 289.6; 39985.4671). This means that they cover the **rational numbers** (which can be represented as the quotient of two integers with a denominator other than zero) and the **irrational numbers** (Those that cannot be expressed as a fraction of whole numbers with a denominator other than zero).

Another classification of real numbers can be made between **algebraic numbers** (a type of complex number) and **transcendent numbers** (a type of irrational number).

More specifically, we find the fact that real numbers are classified into rational and irrational numbers. In the first group there are in turn two categories: the integers, which are divided into three groups (natural, 0, negative integers), and the fractional ones, which are subdivided into proper and improper fraction. All this without forgetting that within the aforementioned natural there are also three varieties: one, natural cousins and natural compounds.

In the second large group mentioned above, that of irrational numbers, we find that there are two classifications: irrational algebraic and inconsequential.

Within Engineering, special use is made of the aforementioned real numbers and it is based on a series of clearly defined ideas such as the following: real numbers are the sum of rational and irrational ones, the set of real ones can be defined as an ordered set and this can be represented by a line in which each point of it represents a specific number.

It is important to keep in mind that real numbers allow you to complete any type of basic operation with two exceptions: the even-order roots of negative numbers are not real numbers (here the notion of complex number appears) and there is no division between zero ( it is not possible to divide something between anything).

This means that with the aforementioned real numbers we can undertake operations such as sums (internal, associative, commutative, opposite element, neutral element ...) or multiplications. In the latter case, it should be stressed that in terms of the multiplication of the signs of the numbers, the result would be the following: + times + equals +; - by - is equal to +; - for + results -; and + by - is equal to -.