Numbers (Meaning and Explanation)

We explain everything about numbers, what types exist and the characteristics of each one. Also, what are sets of numbers.

What are numbers?

Numbers are abstractions, ideas or concepts created by humans to represent, mainly, quantities and magnitudes. Numbers are one of the first inventions of humanity and played an important role in the creation of writing; Since then they have been vital for scientific thought and for the daily life of civilizations.

At the same time, numbers and the relationships between them and with reality constitute a vast field of study, a fundamental part of the discipline of mathematics. There are, thus, various types and categories of numbers, and also different ways of representing them, operations and possible relationships between them, and even philosophical questions about what a number really is.

The word “number”, for its part, comes from Latin numerusmade up of an ancient Indo-European root (nem-), which means “to distribute” or “to distribute”, and the suffix –thatwhich would then become –ero. The ancestral word for “number,” thus, would have been nomesosalso related to other terms such as “norm” or “numismatics”.

Brief history of numbers

numbers history — The first numbers served for the invention of cuneiform writing.

Although it is not easy to find the origin of numbers, that is, of the concept of number itself, it is known that responded to the need to count in the ancestral societies of prehistory. From these civilizations, bones with notches and sets of carvings have been found, which constitutes a clear sign of the primitive need of human beings to establish a system of recording things or the passage of time

The first systems of this type, however, are believed were based on the use of the fingers and toes That's why most number systems have a decimal (10) or vigesimal (20) base.

However, the actual appearance of a written number, that is, of a symbol directly associated with a fixed amount, is a characteristic of more complex societies, such as those that emerged in ancient times, with great capacities for accumulating wealth and tax calculation needs, for commerce, or to compose complex calendars.

It is estimated that The first written numbers appeared 5,000 years ago in Mesopotamia, on clay tablets which also served for the invention of cuneiform writing. In the following centuries, many other ancient cultures created their own methods and systems:

Additives accumulating symbols to express greater value.
Positional in which the order of the symbols expressed a greater or lesser value.
Hybrids which combined the other two trends.

Importance of numbers

numbers importance — Numbers are part of all types of operations that we perform in our daily lives.

The creation of numbers is a central milestone of human civilization, which not only allowed ancient settlers to count and compare sets of things to know which one had more ingredients (for example, which herd has more cows), but also allowed them to leave a record of what was told (for example, how many cows were in the herd yesterday). This may seem like a small thing today, but it is the foundation of almost 10,000 years of study and use of numbers, which has generated new and more complex systems and operations in which to apply them.

So the numbers are today an inseparable part of civilization since they are part of the scientific, logistical, religious and all kinds of operations that we carry out in our daily lives. Without them, there would be no calendars, there would be no computing systems, and humanity would be incapable of carrying out the complex mathematical calculations of which we have been capable throughout history.

Roman numerals and Arabic numerals

Roman and Arabic numerals — Roman numerals use letters of the alphabet to represent exact values.

Since numbers did not have a single common origin, but were the creation of different cultures simultaneously (each of which developed its method, its signs and its own rules of registration), many of these numerical systems became extinct with the passing of the century. time and were replaced by those of the dominant great powers. Hence, today two main sets of numbers are used in the West, that is, two formats of numerical representation: Roman numerals and Arabic numerals.

Roman numerals. Created and developed in Ancient Rome (around the 8th century BC) and used throughout its imperial era, this numbering system used letters of the Roman alphabet to represent exact values, and composed the figures depending on the location of each letter. Thus, for example, the letter I represented one, the V represented five, the they accumulated; except if a letter preceded another of greater value, since in that case they were subtracted: IV represented four, IX represented nine and XC represented ninety. Roman numerals survive today for very specific uses, such as book chapters, century numbers, and other particular uses.
Arabic numerals. Created in India (and therefore really called Indo-Arabic) and transmitted to the Islamic world, this decimal-based numbering system reached the West thanks to the Muslim invasion of southern Europe, and the establishment there of al-Andalus in the Iberian Peninsula. In this system the numbers are represented from one to ten by means of specific glyphs, which changed over time until they became the signs that are used today in almost the entire planet, the well-known 1, 2, 3, 4, 5, 6 , 7, 8, 9 and 0. The logic of these symbols, according to popular opinion, would lie in the total number of angles that each sign has, something that historians however deny. In any case, the construction of figures greater than ten is done by adding numbers to the right, thus going from units to tens and then to hundreds and so on (10, 100, 1000, etc.) always accumulating the value of the written figures.

Cardinal numbers and ordinal numbers

One of the main distinctions that exist between the numbers currently used has to do with what they denote:

Cardinal numbers: indicate quantities
Ordinal numbers: indicate positions.

Prime numbers and composite numbers

Prime numbers are a certain type of particular numbers, greater than 1 and which cannot be divided except by themselves and by unity. This means that they cannot be decomposed into whole numbers, such as 2, 3, 5, 7, 11, 13, 17 or 19.

The prime numbers they are infinite and they appear when counting with a frequency that many mathematicians have found intriguing, which is why they wanted to find the exact pattern that determines when a prime number appears. Between the number 1 and the number 1000, for example, there are 168 prime numbers.

Numbers that are not prime are known as composite numbers. These numbers can be divided by other numbers without giving fractional results. Examples of composite numbers are: 4, 6, 10, 15, 18, 22, etc.

Number sets

sets of numbers — Sets are infinite groupings of numbers that share fundamental properties.

Numbers are studied by Number Theory, a discipline at the service of mathematics, and are often organized in sets, that is, in infinite groupings of numbers that share fundamental properties. These numerical sets are:

Natural numbers (N). Also called counting numbersare those that we use daily and that are used to count, they begin with 0, 1, 2 and end at infinity. Their name is due to the fact that they obey the natural logic of the universe, that is, to the things that exist and that can be counted, such as how many fingers we have on our hand, or how many windows a building has. Natural numbers are classified into cousins and compounds.
Whole numbers (Z). It is a set formed by natural numbers and their negative counterparts, that is, numbers preceded by the minus sign (-) and imaginary located below (or to the left) of zero: -1, -2, -3… -999. Integers, thus, are an infinite set of positive numbers (greater than 0) and negative numbers (less than 0), as long as they are not fractions (hence the name whole). This set is traditionally represented with the letter Z, coming from German Zahlen (“numbers”).
Rational numbers (Q). Both integers and fractional numbers are rational numbers, since this set is understood as the totality of numbers that can be represented as the quotient between an integer and a positive natural number. The set is represented by the letter Q (from quotient“quotient” in several European languages). Examples of rational numbers are: 1, -1, ½, ¼, etc.
Irrational numbers (I). They are numbers whose decimal expression is neither exact nor periodic, that is, they do not comply with the quotient rule to be rational numbers. Numbers with infinite and aperiodic decimals, such as √ 7 or 3.1415918… belong to the irrational numbers, represented as a set by the letter I.
Real numbers (R). It is a set that includes both rational and irrational numbers, that is, any number that can be represented on the number line between minus infinity (negative infinity) and plus infinity (positive infinity) is a real number, regardless of the rest. of its properties. These numbers are represented by the letter R and any number we can think of serves as an example of them.
Complex numbers (C). They are a prolongation or extension of the real numbers, which constitute an algebraically closed body that can be represented as the sum of a real number and an imaginary number. These are numbers that do not “exist” in nature, but rather must be sought and provided by students of pure mathematics through complex equations and calculations applied to other disciplines, such as physics, electronics and engineering.

References

“Number” at https://es.wikipedia.org/
“Etymology of Number” in the Online Spanish Etymological Dictionary. http://etimologias.dechile.net/
“Number sets” in NROC Project. https://content.nroc.org/
“The history of numbers” (video) at the Catholic University of Loja (Ecuador). https://www.youtube.com/
“Number (mathematics)” at https://www.britannica.com/