There are real numbers that are infinite sequences of digits.
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 rational numbers (which can be represented as the quotient of two integers with a denominator other than zero) and irrational numbers (those that cannot be expressed as a fraction of integers with a denominator other than zero).
It should be noted that a number is the expression of a quantity in relation to its unit . The term comes from the Latin numĕrus and refers to a sign or a set of signs .
Origin of the concept of real numbers
Number theory groups these signs into different groups. Natural numbers , for example, include one (1), two (2), three (3), four (4), five (5), six (6), seven (7), eight (8), nine (9) and, generally, to zero (0).
The concept of real numbers arose from the use of common fractions by the Egyptians, around the year 1,000 BC . The development of the notion in mathematics continued with the contributions of the Greeks, who proclaimed the existence of irrational numbers.
Other classifications
Another classification of real numbers can be made between algebraic numbers (a type of complex number) and transcendent numbers (a type of irrational number).
Likewise, real numbers can be distinguished as rational numbers or irrational numbers . In the first group there are two categories: integers , which are divided into three groups ( natural, 0 and negative integers ) and fractionals , which are subdivided into proper fraction and improper fraction. All this without forgetting that within the natural ones there are also three varieties: 1, the natural primes and the natural compounds .
In the group of irrational numbers, meanwhile, we find that there are two classifications within it: algebraic irrational and inconsequential .
The distance between two points can be expressed with real numbers.
Real numbers in engineering
Within engineering , real numbers are especially used. It starts from a series of clearly delimited ideas, such as the following: real numbers are the sum of rational and irrational numbers; the set of reals can be defined as an ordered set; and this can be represented by a line in which each point on 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 roots of even order of negative numbers are not real numbers (here the notion of complex numbers appears) and there is no division by zero ( It is not possible to divide something by nothing).
This means that with real numbers we can undertake operations such as addition (internal, associative, commutative, opposite element, neutral element...) or multiplication . In the latter case it should be emphasized that, with regard to the multiplication of the signs of the numbers , the result would be the following: + for + is equivalent to +; – for – is equal to +; – for + results in -; and + for – is equal to -.
Knowing basic operations (addition, subtraction, multiplication, division) with real numbers is essential for everyday life.
Your expression
The expression of real numbers is carried out with decimals that can sometimes be presented as a sequence of infinite type digits. These decimals are written after the comma or decimal point (that is, to the right).
In some cases, an ellipsis (three consecutive dots) is included at the end of the real number that has decimals. This allows you to indicate that there are other decimals in addition to those already written.
It is important to indicate, taking the latter into account, that the physical sciences express measurements that are approximations to the real number . As a matter of practicality, real numbers, in this framework, are generally written as decimal fractions (proportions). Precision or accuracy, therefore, is not absolute. The same thing happens when rounding is used.
Examples of real numbers
Since the real numbers are infinite , so are the examples that can be mentioned.
Positive numbers are real: therefore, we can mention 5 , 1580 and 6987304 as examples. In turn, the set of real numbers includes the negative ones: -1 , -32 , -896 , -12794335 , etc.
Since irrational numbers are also real numbers, we can indicate examples of this group. In this way, it is possible to name the number e (base of the natural logarithm).
Real numbers, of course, are used in everyday life. Suppose a person enters a pizzeria and orders a mozzarella pizza. The person in charge of the place informs him that the price to pay is 4,500 pesos . As you can see, it communicates the value of the pizza by expressing a real number.
If someone, in a grocery store, requests 2 kilograms of apple , they also appeal to a real number. Just like the traveler who arrives at a hotel and asks for a room for 4 nights .
Real numbers, in short, are used in basic arithmetic calculations. Knowing them and knowing how they are used in various operations is essential to function in different areas.