The need for counting became apparent to man from the very beginning of the formation of a primitive society. Their numerical systems, with specific digital designations, were formed in all isolated centers of civilization: in Egypt and Ancient Babylon, in China and India, among South American Indians and in ancient Greece. Mathematics has gone from simple elementary counting to solving complex topology theorems. Moreover, the history of the number zero counts only a tiny fraction of this period.
Numbers and numbers
From the Latin nullis ("no") came the word denoting one of the most important mathematical concepts. It includes not only a symbol - a number that helps to keep track of, record mathematical operations. This is the whole concept. The absence of any quantity, emptiness, beginning and infinity - the philosophical attitude to these concepts was different in different eras, in different systems of understanding of the world.
Positional number systems
In prehistoric times, fingers and toes helped to keep numbers. The division of numbers into fives and dozens, the origin of the decimal number system is connected with this. In the future, to facilitate these operations, notches on the tree and animal bones, serifs on stones, and pebbles were used. shells and other small items. Each such element denotes a specific number. The most practical numerical models have a similar nature. Such systems are called positional - the value of the digits when writing numbers is determined by their position or discharge.
An example of a system that is opposite in approach and is still used is the method of recording numbers that has come down from the time of Ancient Rome. In it, letters of the Latin alphabet are used to indicate units, tens, hundreds .
Abacus
The counting board, consisting of recesses corresponding to certain categories in which pebbles or beads fit, is familiar to cultures of different peoples and eras. Other varieties of abacus are also known - ropes with knots or cords with beads. The next step in the development of such a device was the scores that were used before the advent of calculators.
The history of the number zero is the process of the emergence of a mathematical concept and the beginning of the application of the symbol denoting it. Both abacus and scores are, in a sense, a means of visualizing a number series. An empty space in the corresponding recess or an absent knuckle on the accounts made the abstract concept of zero clear. The symbol denoting it first appeared among mathematicians and astronomers of Ancient Babylon.
Babylonian Void Sign
In a civilization born between the Tigris and the Euphrates, a numerical system was adopted, inherited from the ancient Sumerians. It was positional - the meaning of the numbers depended on the position relative to other numbers. Developed for 4-5 thousand years BC. e., it was built on the number 60. The mathematical calculations used by the ancient Babylonian engineers and astronomers therefore looked rather cumbersome and uncomfortable. To successfully operate with numbers, it was necessary to remember by heart or have before our eyes the results of multiplying all numbers from 1 to 60.
The number zero, or the sign adopted by the Babylonians to designate a 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 by it.
Overseas zero
Regardless of the mathematicians of Mesopotamia, the Indians of Central America, the Mayans and Incas, introduced their zero into everyday life. Common to both number systems was that they did not develop the idea of zero as a number.
Ancient American civilization has left the world many achievements in the intellectual sphere. Complex calendar systems of the Mayans 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 was their achievements in geometry and astronomy. Numbers in their representation are segments that have a beginning, an end, and a certain length. Zero is a number that has no practical value in this case. The zero-length line in ancient mathematics and philosophy did not make sense.
One of the main tenets 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 is found in the tables of the great astronomer Ptolemy. The letter "Omicron" (the first letter in the word οὐδέν - "nothing") he put in empty cells.
Homeland of Zero - India
What did Indian mathematicians invent? Mahavira (850 g.), Brahmagupta (1114 g.), Ariabhata (476 g.) - authors of treatises in which the modern system of recording numbers and the rules of basic arithmetic operations took shape in many respects. Historians believe that the decimal number system was borrowed by the Indians from the Chinese, and its positional character - from the Babylonians. It is believed that the symbol of zero was also borrowed by the Indians from the works of Ptolemy.
The first of the mathematicians to formulate a complete numerical system, which still remains unchanged and serves most of humanity, was Khorezmi Mohammed bin Musa (787-850), who lived in Baghdad. His “Book on the Indian Account” describes nine Arabic numerals in detail and answered 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 marked the beginning of the spread of eastern mathematical knowledge.
Unlike the Europeans, the eternity of the Eastern philosophers caused awe. Therefore, zero in the equations of ancient Indian scientists finally became not only a symbol of the absence of units in the corresponding category, but also a natural number that affects the result of calculations. Adding zero, multiplying by 0 - all this has gained the meaning of meaningful mathematical operations.
The very spelling of the numbers from 1 to 0 has found its final form also thanks to the ancient Indian mathematical treatises, and those symbols that are commonly called Arabic in Europe are called Arabs by themselves.
The history of the number “zero” is reflected in the etymology of basic mathematical terms. The word "digit" has Arabic roots and comes from the word "al-sifr", which means "empty, zero." The English “zero” is vaguely reminiscent of “marshmallows” - the wind from the east - it was from the East that the finalized, rational and convenient numerical system came to Europe.
Arabic numerals in Europe
One of the main European propagandists of the Arab digital system was the famous Italian mathematician Leonardo Fibonacci. His work The Book of the Abacus (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 merchants. They quickly adopted from the Arab merchants the number system and the writing of numbers. But in European scientific practice, this knowledge tightly entered only after 4 centuries, replacing the ancient system adopted by European mathematicians.
Zero gained importance with the introduction of scientific rectangular coordinate system, proposed in the XVII century by René Descartes. Zero, located in the center, acquired the value of a visible and visually understandable reference point of the three coordinate axes.
In Russia, zero was introduced into practice through the efforts of Leonty Magnitsky, the author of the famous textbook “Arithmetic, or numeral science” (1703).
Zero Properties
Zero, which distinguishes between positive and negative numbers, has unique mathematical properties. This is an even, unsigned natural integer. Adding to zero and subtracting zero does not affect the number, and multiplying by 0 gives zero. Division by zero is considered an operation that does not make sense, which, if executed 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 and led to an unauthorized shutdown of the propulsion system, turned out to be. An incorrect attitude towards a number meaning “nothing” turned a powerful warship into a helpless motionless target.
The value of this number increased significantly with the development of science. Zero arises in areas not only purely mathematical. The audibility threshold in acoustics is taken to be 0. The number at the beginning of the scale of many measuring instruments is also known to the student: 0 on the Celsius scale is the freezing point of water, the origin of longitude is the zero meridian, etc.
Binary numbering, 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 encoded by a combination of two characters - one and zero.
The role of computers in the modern world is becoming crucial for all aspects of life, which means that the history of the number zero, without which their appearance would have been impossible, continues.