The history of the emergence of numbers and mathematical signs. Presentation - the origin of numbers and mathematical signs

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Origin of numbers and mathematical signs

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"People who are not familiar with algebra cannot imagine the amazing things that can be achieved ... with the help of the said science."
G.V. Leibniz

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Significance and development of arithmetic:
Develops human society (?) Actions and rules for actions are studied from elementary school Arithmetic originated from everyday practice Ancient people counted up to 2 (associated this number with the organs of sight and hearing) only much later learned to count up to 3 and then up to 5 With the development of trade the calculation extends to sets Measurement of distances and areas, the capacity of ships there are objects of measurement and rules for working with numbers

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The emergence of numbers
Until now, it is not known exactly who exactly invented the numbers. They say about the numbers that they are Arabic. But what should the Arabs consider in the waterless deserts of Arabia and the Sahara, where they led a nomadic lifestyle?

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Counting machines

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÷ Subtraction
♦ There is an opinion that the signs "+" and "-" originated in trading practice. The vintner marked with dashes how many measures of wine he sold from the barrel. Pouring new reserves into the barrel, he crossed out as many expendable lines as he restored the measures. So, supposedly, there were signs of addition and subtraction in the 15th century. ♦ The inverted Greek letter psi Ψ was used in Greece in the 3rd century BC to denote subtraction. Italian mathematicians used the letter m, the initial letter in the word minus, to do this. ♦ In the 16th century, the “-” sign began to be used to indicate the action of subtraction, and in the 17th century, minus began to be denoted by the sign ÷ to distinguish minus from a dash. This sign is found in the Russian mathematician Leonty Magnitsky at the beginning of the 18th century in his book Arithmetic. ♦ In L. Magnitsky's book, subtraction examples looked like this: 6 ÷ 2 15 ÷ 12

Leonty Filippovich Magnitsky (1669 -1739)

Slide 7

Division:
♦ For thousands of years, the action of division was not indicated by signs. It was simply called and written down in words. ♦ Indian mathematicians were the first to designate division by the initial letter from the name of this action -D. ♦ The Arabs introduced a line to indicate division. It was adopted from the Arabs in the 13th century by the Italian mathematician Fibonacci. He was the first to use the term "private". ♦ The colon (:) sign for division began to be used in the late 17th century. Prior to this, such a sign was also used ÷ ♦ In Russia, the names “divisible”, “divisor”, “private” were first introduced by Leonty Magnitsky at the beginning of the 18th century.
Mathematicians of the Middle Ages.

Slide 8

Common fraction
The first fractions that history introduces us to are fractions of the form: ½; 1/3; ¼ - unit fractions These fractions originated 2000 years ago. Archimedes had other fractions, numbers. We call them mixed. In Russian, the word "fraction" appeared in the 8th century, it came from the verb "crush" - to break into pieces. In the first mathematics textbooks, fractions were called “broken numbers”. The modern designation of fractions originates in ancient India. At first, the fractional line was not used in the notation of fractions. The fraction feature only came into use around 300 years ago. In 1202, the Italian merchant Fibonacci (1170-1250) introduced the word "fraction". The names "numerator" and "denominator" were introduced in the 13th century by Maxim Planud - a Greek monk, scientist, mathematician. In Western Europe, the theory of ordinary fractions was given in 1585 by the Flemish engineer Simon Stevin.

Simon Stevin (1548-1620)
Archimedes (about 287 - -212 BC)

Slide 9

% Percent
♦ This word translated from Latin means "a hundred". ♦ Interest was especially common in Ancient Rome. The Romans called interest the money that the debtor paid for every hundred. For a long time, interest was understood as profit or loss for every hundred rubles. They were used only in commercial and monetary transactions. Then they began to be used both in science and in technology. ♦ There are two opinions about the percent sign. 1. The% sign comes from the Italian word "cento" (one hundred), which was abbreviated cto. In calculations, this word was written very quickly, and gradually the letter t turned into a slash, a symbol appeared to denote a percentage. 2. The percent sign is due to a typo. In 1685, a book on arithmetic was printed in Paris, where by mistake the typesetter typed % instead of cto. After this error, many mathematicians began to use the % sign to represent percentages. Gradually, this sign gained universal recognition.
Robert Record, English mathematician, physician. (1510 - 1558)

Slide 10

Equality =
♦ The equal sign was designated at different times in different ways: both in words and symbols. ♦ The sign “=”, which is very understandable for us, was introduced in 1557 by the English mathematician and physician Robert Record. This is how he explained the choice of sign. “No two objects can be more equal to each other than two parallel lines” ♦ This sign came into general use only in the 18th century, thanks to the German mathematician Wilhelm Leibniz.

Drawing for the book on mathematics by Robert Record "Castle of Knowledge"

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 Multiplication
♦ To denote the action of multiplication, European mathematicians of the 16th century used the letter M, which was the initial in the Latin word for increase, multiplication - multiplication. From this word came the name "cartoon". ♦ In the 17th century, some mathematicians began to denote multiplication with a cross , while others used a period for this. In the 16th and 17th centuries, there was no uniformity in the use of symbols. It wasn't until the late 18th century that most mathematicians used a dot to multiply. ♦ William Outred - English mathematician - in 1631 introduced the multiplication sign with a cross. ♦ The famous German mathematician of the 17th century, Wilhelm Leibniz, used the dot to denote multiplication. ♦ In Europe, for a long time, the product was called the sum of multiplication. The name "multiplier" is mentioned in the works of the 11th century, and "multiplier" in the 13th century. ♦ In Russia, Leonty Magnitsky was the first to give names to the components of multiplication at the beginning of the 18th century.

Wilhelm Leibniz, German mathematician. (1646 - 1716)

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Addition +++
♦ Separate signs for some mathematical concepts appeared in antiquity. However, until the 15th century, there were almost no generally accepted arithmetic signs. ♦ In the 15th and 16th centuries, the Latin letter "P", the initial letter of the word "plus", was used for the addition sign. ♦ For addition, the Latin word "et", meaning "and", was also used. Since the word “et” had to be written very often, they began to shorten it: first they wrote one letter “t”, which gradually turned into a “+” sign. ♦ The ancient Egyptians denoted addition with a sign - a pattern of walking legs. ♦ The name "term" is first found in the works of mathematicians of the 13th century, and the concept of "sum" - in the 15th century. Until that time, the sum was the result of any of the four arithmetic operations. ♦ For the first time, the signs "+" and "-" appear in print in the book "Quick and beautiful account for all merchants." It was written by the Czech mathematician Jan Widman in 1489.
Mathematician. 15th century

Signs

+ - X: =

Warm up:

1. The sum of which three numbers is equal to their product?

2. What part of an hour is 20 minutes?

3. What is the sum of the angles of a square?

4. The perimeter of a square is 20 cm. What is its area?

5. There are 33 students in the class. 24 of them subscribe to the magazine "Funny Pictures", and 14 - to "Murzilka". How many students subscribe to both magazines?

Addition

Until the 15th century, there were almost no generally accepted arithmetic signs.

In the 15th - 16th centuries, the Latin letter was used for the addition sign "P", the initial letter of the word "plus".

For addition, the Latin word "et", meaning "and", was also used. Since the word “et” had to be written very often, they began to shorten it: they wrote one letter first "t" which gradually turned into a sign «+».

The ancient Egyptians denoted addition with a sign - a pattern of walking legs.

The name "term" first occurs in the works of mathematicians of the 13th century, and the concept of "sum" - in the 15th century. Until that time, the sum was the result of any of the four arithmetic operations.

For the first time, the signs "+" and "-" appear in print in the book "A quick and beautiful account for all merchants." It was written by a Czech mathematician Jan Widman in 1489.

Subtraction

There is an opinion that the signs "+" and "-" originated in trading practice. The vintner marked with dashes how many measures of wine he sold from the barrel. Pouring new reserves into the barrel, he crossed out as many expendable lines as he restored the measures. So, supposedly, there were signs of addition and subtraction in the 15th century.

The inverted Greek letter psi was used to denote subtraction in the 3rd century BC. Ψ.

Italian mathematicians used the letter m , the initial letter in the word "minus".

In the 16th century, the “-” sign began to be used to indicate the action of subtraction, and in order to distinguish minus from a dash, in the 17th century, minus began to be denoted by the sign ÷ This sign is found in the Russian mathematician Leonty Magnitsky at the beginning of the 18th century in his book Arithmetic. In the book Leonty Filippovich Magnitsky subtraction examples looked like this: 6 ÷ 2 15 ÷ 12

Multiplication

To denote the operation of multiplication, European mathematicians of the 16th century used the letter M, which was the initial in the Latin word for increase, multiplication, - animation. From this word came the name "cartoon".

In the 16th and 17th centuries, there was no uniformity in the use of symbols. It wasn't until the late 18th century that most mathematicians used a dot to multiply.

William Outred- English mathematician - in 1631 introduced the sign of multiplication with a cross.

The famous German mathematician of the 17th century used the dot to denote multiplication. Wilhelm Leibniz .

In Europe, for a long time, the product was called the sum of multiplication. The name "multiplier" is mentioned in the works of the 11th century, and "multiplier" in the 13th century.

In Russia, he gave names to the components of multiplication for the first time Leonty Magnitsky at the beginning of the 18th century.

Division

For thousands of years, the action of division was not indicated by signs. It was simply called and written down in words.

Indian mathematicians were the first to designate division by the initial letter from the name of this action - D.

The Arabs introduced a line to indicate division. It was adopted from the Arabs in the 13th century by an Italian mathematician fibonacci. He was the first to use the term "private".

The colon sign (:) for division began to be used at the end of the 17th century. Before that, such a sign was also used ÷

In Russia, the names "divisible", "divisor", "private" were first introduced Leonty Magnitsky at the beginning of the 18th century.

Equality

The equal sign was designated at different times in different ways: both in words and symbols.

The “=” sign, which is very understandable for us, was introduced in 1557 by an English mathematician and doctor Robert Record. This is how he explained the choice of sign. "No two things can be more equal to each other than two parallel lines."

This sign came into general use only in the 18th century, thanks to the German mathematician Wilhelm Leibniz.

• in Mexico, cocoa beans were money;
• in Canada, Alaska and Siberia, ancient ancestors used the skins of valuable animals as money;
• among some tribes of South America and on the islands of Oceania, seashells or pearls were money;
• New Zealand tribes used stones with a hole in the middle instead of money.

Metal money is easy to store and transport.

Paper money - appeared in 910 in China. And in Russia, the first paper money was introduced under Catherine II in 1769.

Topic: "Symbols and signs"

Objective: Create an emblem for the Clever and Clever Club using different symbols and signs so that others understand it.

When people interact for a long time within a certain area of ​​activity, they begin to look for a way to optimize the communication process. The system of mathematical signs and symbols is an artificial language that was designed to reduce the amount of graphically transmitted information and at the same time fully preserve the meaning inherent in the message.

Any language requires learning, and the language of mathematics in this regard is no exception. To understand the meaning of formulas, equations and graphs, it is required to have certain information in advance, to understand the terms, notation, etc. In the absence of such knowledge, the text will be perceived as written in an unfamiliar foreign language.

In accordance with the demands of society, graphic symbols for simpler mathematical operations (for example, the notation of addition and subtraction) were developed earlier than for complex concepts like the integral or differential. The more complex the concept, the more complex sign it is usually denoted.

Models for the formation of graphic symbols

In the early stages of the development of civilization, people associated the simplest mathematical operations with their familiar concepts based on associations. For example, in ancient Egypt, addition and subtraction were indicated by a pattern of walking legs: lines directed in the direction of reading indicated “plus”, and in the opposite direction - “minus”.

Numbers, perhaps, in all cultures, were originally indicated by the corresponding number of dashes. Later, conventions began to be used for recording - this saved time, as well as space on tangible media. Often letters were used as symbols: this strategy has become widespread in Greek, Latin and many other languages ​​​​of the world.

The history of the emergence of mathematical symbols and signs knows the two most productive ways of forming graphic elements.

Word Representation Transformation

Initially, any mathematical concept is expressed by some word or phrase and does not have its own graphical representation (other than lexical). However, performing calculations and writing formulas in words is a lengthy procedure and takes up an unreasonably large amount of space on a material carrier.

A common way to create mathematical symbols is to transform the lexical representation of a concept into a graphic element. In other words, the word denoting a concept is shortened or transformed in some other way over time.

For example, the main hypothesis of the origin of the plus sign is its abbreviation from the Latin et, whose analogue in Russian is the union "and". Gradually, in cursive writing, the first letter ceased to be written, and t reduced to a cross.

Another example is the "x" sign for the unknown, which was originally an abbreviation for the Arabic word for "something". Similarly, there were signs for the square root, percent, integral, logarithm, etc. In the table of mathematical symbols and signs, you can find more than a dozen graphic elements that appeared in this way.

Arbitrary character assignment

The second common variant of the formation of mathematical signs and symbols is the assignment of a symbol in an arbitrary way. In this case, the word and the graphic designation are not related to each other - the sign is usually approved as a result of the recommendation of one of the members of the scientific community.

For example, the signs for multiplication, division, and equality were proposed by the mathematicians William Oughtred, Johann Rahn, and Robert Record. In some cases, several mathematical signs could be introduced into science by one scientist. In particular, Gottfried Wilhelm Leibniz proposed a number of symbols, including the integral, differential, and derivative.

The simplest operations

Signs such as plus and minus, as well as symbols for multiplication and division, are known to every student, despite the fact that there are several possible graphic signs for the last two operations mentioned.

It is safe to say that people knew how to add and subtract many millennia BC, but standardized mathematical signs and symbols that denote these actions and are known to us today appeared only by the XIV-XV century.

However, despite the establishment of a certain agreement in the scientific community, multiplication in our time can be represented by three different signs (diagonal cross, dot, asterisk), and division by two (a horizontal line with dots above and below or a slash).

Letters

For many centuries, the scientific community has used Latin exclusively for the exchange of information, and many mathematical terms and signs find their origins in this language. In some cases, graphic elements have become the result of abbreviation of words, less often - their intentional or accidental transformation (for example, due to a typo).

The designation of the percentage ("%"), most likely, comes from the erroneous spelling of the abbreviation who(cento, i.e. "hundredth part"). In a similar way, the plus sign, the history of which is described above, occurred.

Much more was formed by intentionally shortening the word, although this is not always obvious. Not every person recognizes the letter in the square root sign R, i.e. the first character in the word Radix ("root"). The integral symbol also represents the first letter of the word Summa, but it is intuitively similar to a capital letter. f without a horizontal line. By the way, in the first publication, the publishers made just such a mistake by typing f instead of this character.

Greek letters

As graphic symbols for various concepts, not only Latin ones are used, but also in the table of mathematical symbols you can find a number of examples of such a name.

The number Pi, which is the ratio of the circumference of a circle to its diameter, comes from the first letter of the Greek word for circle. There are several lesser known irrational numbers, denoted by the letters of the Greek alphabet.

An extremely common sign in mathematics is the "delta", which reflects the amount of change in the value of variables. Another common sign is "sigma", which acts as a sum sign.

Moreover, almost all Greek letters are used in one way or another in mathematics. However, these mathematical signs and symbols and their meaning are known only to people who are engaged in science professionally. In everyday life and everyday life, this knowledge is not required for a person.

Signs of logic

Oddly enough, many intuitive symbols have been invented only recently.

In particular, the horizontal arrow, replacing the word "therefore", was proposed only in 1922. The quantifiers of existence and universality, i.e., the signs read as: "exists ..." and "for any ..." were introduced in 1897 and 1935 respectively.

Symbols from the field of set theory were invented in 1888-1889. And the crossed out circle, which today is known to any high school student as a sign of an empty set, appeared in 1939.

Thus, signs for such complex concepts as the integral or the logarithm were invented centuries earlier than some intuitive symbols that are easily perceived and assimilated even without prior preparation.

Mathematical symbols in English

Due to the fact that a significant part of the concepts was described in scientific works in Latin, a number of names of mathematical signs and symbols in English and Russian are the same. For example: Plus (“plus”), Integral (“integral”), Delta function (“delta function”), Perpendicular (“perpendicular”), Parallel (“parallel”), Null (“zero”).

Some of the concepts in the two languages ​​are called differently: for example, division is Division, multiplication is Multiplication. In rare cases, the English name for a mathematical sign gets some distribution in Russian: for example, a slash in recent years is often referred to as a "slash" (English Slash).

symbol table

The easiest and most convenient way to get acquainted with the list of mathematical signs is to look at a special table that contains the signs of operations, symbols of mathematical logic, set theory, geometry, combinatorics, mathematical analysis, linear algebra. This table shows the main mathematical signs in English.

Math symbols in a text editor

When performing various kinds of work, it is often necessary to use formulas that use characters that are not on the computer keyboard.

Like graphic elements from almost any field of knowledge, mathematical signs and symbols in Word can be found in the Insert tab. In the 2003 or 2007 versions of the program, there is the “Insert Symbol” option: when you click on the button on the right side of the panel, the user will see a table that contains all the necessary mathematical symbols, Greek lowercase and uppercase letters, various types of brackets and much more.

In versions of the program released after 2010, a more convenient option has been developed. When you click on the "Formula" button, you go to the formula designer, which provides for the use of fractions, entering data under the root, changing the case (to indicate degrees or ordinal numbers of variables). All signs from the table presented above can also be found here.

Is it worth learning math symbols

The system of mathematical notation is an artificial language that only simplifies the recording process, but cannot bring understanding of the subject to an outside observer. Thus, memorizing signs without studying terms, rules, logical connections between concepts will not lead to mastering this area of ​​knowledge.

The human brain easily learns signs, letters and abbreviations - mathematical notations are remembered by themselves when studying the subject. Understanding the meaning of each specific action creates so strong that the signs denoting the terms, and often the formulas associated with them, remain in memory for many years and even decades.

Finally

Since any language, including an artificial one, is open to changes and additions, the number of mathematical signs and symbols will certainly grow over time. It is possible that some elements will be replaced or adjusted, while others will be standardized in the only possible way, which is relevant, for example, for multiplication or division signs.

The ability to use mathematical symbols at the level of a full school course is practically necessary in the modern world. In the context of the rapid development of information technology and science, the widespread algorithmization and automation, the possession of a mathematical apparatus should be taken as a given, and the development of mathematical symbols as an integral part of it.

Since calculations are used in the humanitarian sphere, and in economics, and in the natural sciences, and, of course, in the field of engineering and high technology, understanding mathematical concepts and knowledge of symbols will be useful for any specialist.

Ministry of Education of the Republic of Mordovia State Budgetary Vocational Educational Institution of the Republic of Mordovia "Krasnoslobodsky Agrarian College"

Related presentation

"History of Mathematical Signs"

educational teacher

disciplines "Mathematics"

Goals

explore the history of the emergence of mathematical signs

find out the role of signs in the progress of mathematical knowledge

organize the acquisition of knowledge using diagrams and tables

study information sources

explore the key concepts of the topic "History of Mathematical Signs" using concept trees

analyze the history of the emergence of mathematical signs

make inferential knowledge on them and determine the boundaries of the study

Numbers are the first mathematical signs

The first written numbers, of which we have reliable evidence, appeared in Egypt and Mesopotamia about 5000 years ago.

This is what the number plates looked like in Mesopotamia

The gradual transformation of the original figures into modern figures:

The ancient Romans used a number system to display numbers as letters. They used the following letters in their number system: I.V.L.C.D.M. Each letter had a different meaning, each digit corresponded to the position number of the letter.

Therefore, Peter I introduced ten digits familiar to us in Russia, canceling the alphabetic digit.

The Slavs designated large numbers in the following way:

Ten thousand is darkness

ten themes are legion,

ten legions - leodrus,

ten leodres - raven,

ten ravens - deck

Addition and subtraction signs

• The plus and minus signs were apparently invented in the German mathematical school of "kossists" (that is, algebraists). They are used in Johann Widmann's Arithmetic, published in 1489. Prior to this, addition was denoted by the letter p (plus) or the Latin word et (conjunction "and"), and subtraction - by the letter m (minus). In Widman, the plus symbol replaces not only addition, but also the union "and". The origin of these symbols is unclear, but most likely they were previously used in trading as signs of profit and loss. Both symbols almost instantly gained general distribution in Europe - with the exception of Italy, which used the old designations for about a century.

Multiplication and division signs

The multiplication sign was introduced in 1631 by William Outred (England)

in the form of an oblique cross. Before it was used

rectangle symbol (Erigon, 1634),

asterisk (Johann Rahn, 1659). Later in 1698.

G. Leibniz replaced the cross with a dot,

not to be confused with the letter x; before him

symbolism was found in Regiomontanus (XV century) and the English scientist

Thomas Harriot

Distribution in England and USA

received the symbol ÷ (obelus), which

suggested Johann Rahn and

John Pell in 1659

Decimal point

• Separating the fractional part of a number from the integer, the decimal point was introduced by the Italian astronomer Magini (1592) and Napier (1617). Previously, other characters were used instead of a comma - a vertical bar: 3|62, or a zero in brackets: 3 (0) 62; some authors, following al-Kashi, used ink of different colors. In England, instead of a comma, they preferred to use a period, which was placed in the middle of the line; this tradition was adopted in the USA, but the dot was moved down so as not to be confused with the multiplication sign.

Common fraction

• The usual “two-story” record of an ordinary fraction, which is familiar to us, was used by ancient Greek mathematicians, although their denominator was written above the numerator, and there was no line of the fraction. Indian mathematicians have moved the numerator up; through the Arabs, this format was adopted in Europe. The fractional line was first introduced in Europe by Leonardo of Pisa (1202)

but she only came into use

supported by Johann Widmann (1489).

The % sign was fixed to denote percent in the 17th century. It probably came from the contraction of the Latin word "centum" in "cto". In cursive, "cto" began to look like "o / o", and then - "%".

Signs of operations and relations

• Equal sign . It was proposed by Robert Record in 1557.

The inscription of the symbol was much longer than the current one.

parallel segments of the same length. some time

the spread of the Record symbol was hindered by the fact that

that since ancient times the same symbol has been used

to indicate the parallelism of lines; eventually

it was decided to make the symbol of parallelism vertical.

In continental Europe, the equal sign was introduced by G. Leibniz.

Exponentiation

Girard

• The modern notation of the exponent was introduced by Descartes

in his "Geometry" (1637), however, only for natural

degrees greater than two. Later Newton

distributed this form

records for negative

and fractional exponents (1676),

the interpretation of which by this time had already been proposed

Stevin

Wallis

Sign of the logarithm

• Until the end of the 19th century, there was no generally accepted notation for the logarithm, the base a indicated to the left and above the symbol log , then over it. Ultimately, mathematicians came to the conclusion that the most convenient place for the base is below the line, after the symbol log . Brief designations of the most common types of logarithm - decimal and natural - appeared much earlier at once by several authors and were finally fixed also by the end of the 19th century.

Notation for trigonometric functions

• Abbreviations for sine and cosine

introduced by William Outred in the middle of the 17th century.

Abbreviations for tangent

and cotangent: introduced by Johann Bernoulli

In the XVIII century, they became widespread in Germany and Russia.

In other countries, the names of these functions are used,

proposed by Albert Girard even earlier, at the beginning of the 17th century

Round brackets

• Appeared at Tartaglia (1556)

(for root expression)

and later with Girard. Simultaneously

Bombelli used as

initial bracket corner in the form

the letter L, and as the final -

his inverted form (1550); such a record became the progenitor of square brackets. Curly brackets were proposed by F. Viet (1593).

Comparison signs

Introduced by Thomas Harriot

in his essay, published posthumously

in 1631. Before him they wrote: more , smaller .

Non-strict comparison symbols suggested

Wallis in 1670.

Initially, the bar was above the comparison sign, and not below it, as it is now. These symbols became common after

support of the French mathematician Pierre Bouguer (1734), from whom they acquired a modern look.

Integral notation

• G. Leibniz produced the words "Sum" from the first letter ( Summa). Newton in his works did not offer an alternative symbolism of the integral, although he tried various options: a vertical bar over a function or a square symbol that stands in front of a function or borders it. The term itself integral invented by Jacob Bernoulli (1690).

Designation of differential, derivative

• A significant part of the commonly used symbols of mathematical analysis belongs to G. Leibniz.

• The brief designation of the derivative with a prime goes back to J. Lagrange.

Limit notation

• The symbol of the limit appeared in 1787 with Simon Lhuillier and was supported by O. Cauchy (1821)

Argument Limit

first mentioned separately, after

symbol lim, not below it. close to

introduced the modern designation

Weierstrass.

However, instead of the usual arrow, he used the equal sign. The arrow appeared at the beginning of the 20th century in several mathematicians at once, for example, in Hardy (1908).

Symbolism of set theory

• It was greatly influenced by the symbolism of mathematical logic, closely related to it and already well developed by the end of the 19th century. The set-theoretic symbols "contains" and "contains" appeared in 1890 with the German logician Ernst Schroeder. At first, the relations “contained” and “is an element” were not distinguished, but even before the paradoxes of set theory appeared, a separate membership symbol began to be used by Giuseppe Peano

(1895, from Greek εστι, be). He is also the author

symbols of intersection and union of sets (1888).

Information sources

• Balyazin V. “Encyclopedia. Wisdom of millennia”, M., 2004.
• Great Mathematical Encyclopedia, edited by Yakusheva G.M., M., 2005.
• Glazer G.I. "History of mathematics at school", M., 1998.
• Golovanov Y. "Etudes about scientists", M., 1997.
• Depman I. "The World of Numbers", L., 1996.
• Ozhegov S.I. "Dictionary of the Russian language", M., 2002.
• Raik A.E. "Essays on the history of mathematics in antiquity", Mordovian book publishing house, Saransk, 1999.
• "Encyclopedic Dictionary of a Young Mathematician" edited by Gnedko B.V., M., 2003.