### Education, Secondary education and schools

# The history of the number zero. What is the number 0?

The need for calculation has become evident to man from the very beginning of the formation of primitive society. Their numerical systems, with specific digital notations, were formed in all isolated centers of civilization: in Egypt and Ancient Babylon, in China and India, among the South American Indians and in ancient Greece. Mathematics passed from the simplest calculation of objects to the solution of the most complicated topology theorems. At the same time, the history of the number zero has only a scanty part of this period.

## Numbers and numbers

From the Latin nullis ("no") there was a word denoting one of the most important mathematical concepts. It includes not only a symbol - a digit that helps to keep score, record mathematical operations. This is a whole concept. The absence of any number, emptiness, the beginning and infinity - the philosophical relation to these concepts was different in different epochs, in different systems of world outlook.

## Positional number systems

In prehistoric times, the calculus was assisted by fingers and toes. The division of numbers into fives and tens, the origin of the decimal number system is connected with this. In the future, to facilitate these operations in the course were notches on the tree and bones of animals, notches on stones, pebbles. Shells and other small items. Each such element denotes a specific number. The most practical numeric models have a similar nature. Such systems are called positional systems - the value of numbers when writing numbers is determined by their position or digit.

An example of the opposite in approach and the system used so far is the method of writing numbers, which has survived since the days of Ancient Rome. In it, for the designation of units, tens, hundreds, the letters of the Latin alphabet are used .

## Abacus

A counting board consisting of depressions corresponding to certain categories, in which pebbles or beads are laid, is familiar to cultures of different peoples and epochs. Other varieties of the abaca are also known - rope with knots or cords with beads. The next step in the development of such an adaptation was the scores used before the calculators appeared.

The history of the number zero is the process of the emergence of a mathematical concept and the beginning of the use of the symbol that designates it. And the abacus, and the counts are in a sense a means of visualizing the numerical series. An empty place in the corresponding depression or an absent knuckle on the accounts made the abstract concept of zero visible. The symbol denoting it first appeared in mathematicians and astronomers of Ancient Babylon.

## Babylonian emblem of emptiness

In the civilization born in the interfluve of the Tigris and the Euphrates, a numerical system was adopted, inherited from the ancient Sumerians. It was positional - the value of the numbers depended on the position relative to other numbers. Developed for 4-5 thousand years BC. It was built on the number 60. The mathematical calculations used by the ancient Babylonian engineers and astronomers, therefore, looked rather cumbersome and inconvenient. To successfully operate with numbers, it was necessary to remember by heart or to have the results of multiplication of all numbers from 1 to 60 before your eyes.

The numeral zero, or the sign adopted by the Babylonians to indicate the discharge, looked like two wedges or arrows set at an angle. This symbol was an integral part of the number and did not participate in arithmetic operations - it was impossible to add or multiply it.

## Overseas Zero

Regardless of the mathematicians of Mesopotamia, Zero Indians of Central America, the Maya and the Incas, were introduced into use. Common to both number systems was that they did not develop the idea of zero as a number.

Ancient American civilization left a lot of achievements in the intellectual sphere to the world. Complex calendar systems of Maya and Incas are the result of centuries of experience in astronomical observations and complex mathematical calculations. But never in their equations the number zero was not present as a number that affects the result of mathematical operations.

## Antique look

The main legacy of the ancient Greek mathematicians were their achievements in geometry and astronomy. The numbers in their representation are segments having a beginning, an end, and a certain length. Zero is a number that does not have practical value in this case. A segment with zero length in ancient mathematics and philosophy did not make sense.

One of the main postulates of Aristotle's teaching is the phrase Natura abhorret vacuum - "Nature does not tolerate emptiness." Infinity, nothing, nonexistence - these categories did not fit into the ancient universe. Therefore, the modern meaning of the question "what number is 0" was unattainable for Archimedes, Pythagoras or Euclid, although a symbol similar to zero occurs in the tables of the great astronomer Ptolemy. The letter "Omicron" (the first letter in the word οὐδέν - "nothing"), he put in empty cages.

## Homeland of Nil - India

What did the Indian mathematicians invent? Mahavira (850), Brahmagupta (1114), Aryabhata (476) - the authors of treatises, in which the modern system of writing numbers and the rules of basic arithmetic operations have largely taken shape. Historians believe that the decimal number system was borrowed by the Indians from the Chinese, and the positional character of it - from the Babylonians. There is an opinion that the symbol of zero was also borrowed by the Indians from the works of Ptolemy.

The first of the mathematicians who formulated the complete numerical system, which still remains unchanged and serves the greater part of humanity, was Khorezmi Muhammad bin Musa (787-850), who lived in Baghdad. In his "Book of the Indian Account", nine Arab numerals are described in detail and the answer to the question: "Is 0 a number?" The mention of zero in this book is considered the first. The Latin translation of this work became widely known in Europe in the 12th century and initiated the dissemination of oriental mathematical knowledge.

Unlike Europeans, the eternity of Eastern philosophers aroused awe. Therefore zero in the equations of ancient Indian scientists finally became not only a symbol of the absence of units in the corresponding discharge, but also a natural number that affects the result of calculations. Adding zero, multiplying by 0 - all this gained the meaning of meaningful mathematical operations.

The very writing of the figures from 1 to 0 has found its final form, too, thanks to ancient Indian mathematical treatises, and those symbols, which in Europe are commonly called Arabic, are called by the Arabs themselves Indian.

The history of the number "zero" was reflected in the etymology of the basic mathematical terms. The word "figure" has Arabic roots and comes from the word "al-cifr", which means "empty, zero". The English "zero" remotely resembles "marshmallow" - the wind from the east - it was from the East that a definitively designed, rational and convenient numerical system came to Europe.

## Arab figures in Europe

One of the main European propagandists of the Arab digital system was the famous Italian mathematician Leonardo Fibonacci. His work The Abacus Book (1202) introduced European scholars to the symbols and rules by which Arabs record mathematical operations. The first convenience and rationality of the eastern mathematical model was appreciated by those who are accustomed to the daily handling of numbers - bankers and traders. They quickly adopted from the Arab merchants number system and the writing of numbers. But in the scientific practice of Europe, this knowledge densely entered only four centuries later, replacing the ancient system adopted by European mathematicians.

An important value of zero was found with the introduction into scientific use of a rectangular coordinate system, proposed in the XVII century by Rene Descartes. Zero, located in the center, has acquired the value of a visible and visually understandable reference point for the three axes of coordinates.

In Russia, zero was put into practice by the efforts of Leonty Magnitsky, the author of the famous textbook "Arithmetic, the Science of Numbers" (1703).

## Properties of zero

Zero, which distinguishes between positive and negative numbers, has unique mathematical properties. This is an even, non-signed natural integer. Adding with zero and subtracting zero does not affect the number in any way, and multiplying by 0 gives zero. Division by zero is considered to be a meaningless operation, which, if performed in a computer program, can cause significant harm to the system.

It was in the attempt to divide by 0 that the meaning of the failure in the computer system of the US Navy cruiser Yorktown, which occurred in the fall of 1997, resulted in an unauthorized shutdown of the propulsion system. A clumsy attitude toward a number meaning "nothing" turned a powerful warship into a helpless stationary target.

The significance of this number has increased significantly with the development of science. Zero arises in areas not only purely mathematical. The threshold of audibility in acoustics is taken as 0. What number is at the beginning of the scale of many measuring instruments, it is also known to the student: 0 on the Celsius scale - the freezing point of water, the origin of the longitude - the zero meridian, etc.

Binary notation, which served as the basis for the creation of modern computing devices, is a positional number system with a base of two. This means that all data entered into computer systems is coded by a combination of two characters - one and zero.

The role of computers in the modern world becomes decisive for all aspects of life, which means that the history of the number zero, without which their appearance would be impossible, continues.

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