Negative numbers - why do children study something that does not exist? What numbers are called positive and negative. Negative numbers are
Positive and negative numbers
Coordinate line
Let's go straight. Let's mark point 0 (zero) on it and take this point as the starting point.
We indicate with an arrow the direction of movement in a straight line to the right from the origin of coordinates. In this direction from point 0 we will plot positive numbers.
That is, numbers that are already known to us, except zero, are called positive.
Sometimes positive numbers are written with a “+” sign. For example, "+8".
For brevity, the “+” sign before a positive number is usually omitted and instead of “+8” they simply write 8.
Therefore, “+3” and “3” are the same number, only designated differently.
Let's choose some segment whose length we take as one and move it several times to the right from point 0. At the end of the first segment the number 1 is written, at the end of the second - the number 2, etc. 
Putting the unit segment to the left from the origin we get negative numbers: -1; -2; etc.
Negative numbers
used to denote various quantities, such as: temperature (below zero), flow - that is, negative income, depth - negative height, and others.
As can be seen from the figure, negative numbers are numbers already known to us, only with a minus sign: -8; -5.25, etc.
- The number 0 is neither positive nor negative.
The number axis is usually positioned horizontally or vertically.
If the coordinate line is located vertically, then the direction up from the origin is usually considered positive, and the direction down from the origin is negative.
The arrow indicates the positive direction.
The straight line marked:
. origin (point 0);
. unit segment;
. the arrow indicates the positive direction;
called coordinate line
or number axis.
Opposite numbers on a coordinate line
Let us mark two points A and B on the coordinate line, which are located at the same distance from point 0 on the right and left, respectively.
In this case, the lengths of the segments OA and OB are the same.
This means that the coordinates of points A and B differ only in sign. 
Points A and B are also said to be symmetrical about the origin.
The coordinate of point A is positive “+2”, the coordinate of point B has a minus sign “-2”.
A (+2), B (-2).
- Numbers that differ only in sign are called opposite numbers. The corresponding points of the numerical (coordinate) axis are symmetrical relative to the origin.
Every number has only one opposite number. Only the number 0 does not have an opposite, but we can say that it is the opposite of itself.
The notation "-a" means the opposite number of "a". Remember that a letter can hide either a positive number or a negative number.
Example:
-3 is the opposite number of 3.
We write it as an expression:
-3 = -(+3)
Example:
-(-6) is the opposite number to the negative number -6. So -(-6) is a positive number 6.
We write it as an expression:
-(-6) = 6
Adding Negative Numbers
The addition of positive and negative numbers can be analyzed using the number line.
It is convenient to perform the addition of small modulo numbers on a coordinate line, mentally imagining how the point denoting the number moves along the number axis.
Let's take some number, for example, 3. Let's denote it on the number axis by point A.
Let's add the positive number 2 to the number. This will mean that point A must be moved two unit segments in the positive direction, that is, to the right. As a result, we get point B with coordinate 5.
3 + (+ 2) = 5
In order to add a negative number (- 5) to a positive number, for example, 3, point A must be moved 5 units of length in the negative direction, that is, to the left.
In this case, the coordinate of point B is - 2.
So, the order of addition rational numbers using a number axis would be:
. mark a point A on the coordinate line with a coordinate equal to the first term;
. move it a distance equal to the modulus of the second term in the direction that corresponds to the sign in front of the second number (plus - move to the right, minus - to the left);
. the point B obtained on the axis will have a coordinate that will be equal to the sum of these numbers.
Example.
- 2 + (- 6) =
Moving from point - 2 to the left (since there is a minus sign in front of 6), we get - 8.
- 2 + (- 6) = - 8
Adding numbers with the same signs
Adding rational numbers can be easier if you use the concept of modulus.
Let us need to add numbers that have the same signs.
To do this, we discard the signs of the numbers and take the modules of these numbers. Let's add the modules and put the sign in front of the sum that was common to these numbers.
Example. 
An example of adding negative numbers.
(- 3,2) + (- 4,3) = - (3,2 + 4,3) = - 7,5
- To add numbers of the same sign, you need to add their modules and put in front of the sum the sign that was before the terms.
Adding numbers with different signs
If the numbers have different signs, then we act somewhat differently than when adding numbers with the same signs.
. We discard the signs in front of the numbers, that is, we take their modules.
. From the larger module we subtract the smaller one.
. Before the difference we put the sign that was in the number with a larger module.
An example of adding a negative and a positive number.
0,3 + (- 0,8) = - (0,8 - 0,3) = - 0,5
An example of adding mixed numbers.
To add numbers of different signs you need:
. subtract the smaller module from the larger module;
. Before the resulting difference, put the sign of the number with the larger modulus.
Subtracting Negative Numbers
As you know, subtraction is the opposite of addition.
If a and b are positive numbers, then subtracting the number b from the number a means finding a number c that, when added to the number b, gives the number a.
a - b = c or c + b = a
The definition of subtraction holds true for all rational numbers. That is subtracting positive and negative numbers can be replaced by addition.
- To subtract another from one number, you need to add the opposite number to the one being subtracted.
Or, in another way, we can say that subtracting the number b is the same as addition, but with the opposite number to b.
a - b = a + (- b)
Example.
6 - 8 = 6 + (- 8) = - 2
Example.
0 - 2 = 0 + (- 2) = - 2
- It is worth remembering the expressions below.
- 0 - a = - a
- a - 0 = a
- a - a = 0
Rules for subtracting negative numbers
As can be seen from the examples above, subtracting a number b is an addition with a number opposite to b.
This rule holds true not only when subtracting a smaller number from a larger number, but also allows you to subtract a larger number from a smaller number, that is, you can always find the difference of two numbers.
The difference can be a positive number, a negative number, or a zero number.
Examples of subtracting negative and positive numbers.
. - 3 - (+ 4) = - 3 + (- 4) = - 7
. - 6 - (- 7) = - 6 + (+ 7) = 1
. 5 - (- 3) = 5 + (+ 3) = 8
It is convenient to remember the sign rule, which allows you to reduce the number of parentheses.
The plus sign does not change the sign of the number, so if there is a plus in front of the parenthesis, the sign in the parentheses does not change.
+ (+ a) = + a
+ (- a) = - a
The minus sign in front of the parentheses reverses the sign of the number in the parentheses.
- (+ a) = - a
- (- a) = + a
From the equalities it is clear that if there are identical signs before and inside the brackets, then we get “+”, and if the signs are different, then we get “-”.
(- 6) + (+ 2) - (- 10) - (- 1) + (- 7) = - 6 + 2 + 10 + 1 - 7 = - 13 + 13 = 0
The rule of signs is preserved even if there is not one number in brackets, but algebraic sum numbers.
a - (- b + c) + (d - k + n) = a + b - c + d - k + n
Please note that if there are several numbers in brackets and there is a minus sign in front of the brackets, then the signs in front of all the numbers in these brackets must change.
To remember the rule of signs, you can create a table for determining the signs of a number.
Sign rule for numbers
Or learn a simple rule.
- Two negatives make an affirmative,
- Plus times minus equals minus.
Multiplying Negative Numbers
Using the concept of the modulus of a number, we formulate the rules for multiplying positive and negative numbers.
Multiplying numbers with the same signs
The first case that you may encounter is the multiplication of numbers with the same signs.
To multiply two numbers with the same signs:
. multiply the modules of numbers;
. put a “+” sign in front of the resulting product (when writing the answer, the “plus” sign before the first number on the left can be omitted).
Examples of multiplying negative and positive numbers.
. (- 3) . (- 6) = + 18 = 18
. 2 . 3 = 6
Multiplying numbers with different signs
The second possible case is the multiplication of numbers with different signs.
To multiply two numbers with different signs:
. multiply the modules of numbers;
. Place a “-” sign in front of the resulting work.
Examples of multiplying negative and positive numbers.
. (- 0,3) . 0,5 = - 1,5
. 1,2 . (- 7) = - 8,4
Rules for multiplication signs
Remembering the sign rule for multiplication is very simple. This rule coincides with the rule for opening parentheses.
- Two negatives make an affirmative,
- Plus times minus equals minus.
In “long” examples, in which there is only a multiplication action, the sign of the product can be determined by the number of negative factors.
At even number of negative factors, the result will be positive, and with odd quantity - negative.
Example.
(- 6) . (- 3) . (- 4) . (- 2) . 12 . (- 1) =
There are five negative factors in the example. This means that the sign of the result will be “minus”.
Now let's calculate the product of the moduli, not paying attention to the signs.
6 . 3 . 4 . 2 . 12 . 1 = 1728
The end result of multiplying the original numbers will be:
(- 6) . (- 3) . (- 4) . (- 2) . 12 . (- 1) = - 1728
Multiplying by zero and one
If among the factors there is a number zero or positive one, then the multiplication is performed according to known rules.
. 0 . a = 0
. a. 0 = 0
. a. 1 = a
Examples:
. 0 . (- 3) = 0
. 0,4 . 1 = 0,4
Negative one (- 1) plays a special role when multiplying rational numbers.
- When multiplied by (- 1), the number is reversed.
IN literal expression this property can be written:
a. (- 1) = (- 1) . a = - a
When adding, subtracting and multiplying rational numbers together, the order of operations established for positive numbers and zero is maintained.
An example of multiplying negative and positive numbers.
Dividing negative numbers
It's easy to understand how to divide negative numbers by remembering that division is the inverse of multiplication.
If a and b are positive numbers, then dividing the number a by the number b means finding a number c that, when multiplied by b, gives the number a.
This definition of division applies to any rational numbers as long as the divisors are non-zero.
Therefore, for example, dividing the number (- 15) by the number 5 means finding a number that, when multiplied by the number 5, gives the number (- 15). This number will be (- 3), since
(- 3) . 5 = - 15
Means
(- 15) : 5 = - 3
Examples of dividing rational numbers.
1. 10: 5 = 2, since 2 . 5 = 10
2. (- 4) : (- 2) = 2, since 2 . (- 2) = - 4
3. (- 18) : 3 = - 6, since (- 6) . 3 = - 18
4. 12: (- 4) = - 3, since (- 3) . (- 4) = 12
From the examples it is clear that the quotient of two numbers with the same signs is a positive number (examples 1, 2), and the quotient of two numbers with different signs is a negative number (examples 3,4).
Rules for dividing negative numbers
To find the modulus of a quotient, you need to divide the modulus of the dividend by the modulus of the divisor.
So, to divide two numbers with the same signs, you need to:
. Place a “+” sign in front of the result.
Examples of dividing numbers with the same signs:
. (- 9) : (- 3) = + 3
. 6: 3 = 2
To divide two numbers with different signs, you need to:
. divide the module of the dividend by the module of the divisor;
. Place a “-” sign in front of the result.
Examples of dividing numbers with different signs:
. (- 5) : 2 = - 2,5
. 28: (- 2) = - 14
You can also use the following table to determine the quotient sign.
Rule of signs for division
When calculating “long” expressions in which only multiplication and division appear, it is very convenient to use the sign rule. For example, to calculate a fraction
Please note that the numerator has 2 minus signs, which when multiplied will give a plus. There are also three minus signs in the denominator, which when multiplied will give a minus sign. Therefore, in the end the result will turn out with a minus sign.
Reducing a fraction ( further actions with moduli of numbers) is performed in the same way as before:
- The quotient of zero divided by a number other than zero is zero.
- 0: a = 0, a ≠ 0
- You CANNOT divide by zero!
All previously known rules of division by one also apply to the set of rational numbers.
. a: 1 = a
. a: (- 1) = - a
. a: a = 1
, where a is any rational number.
The relationships between the results of multiplication and division, known for positive numbers, remain the same for all rational numbers (except zero):
. if a . b = c; a = c: b; b = c: a;
. if a: b = c; a = c. b; b = a: c
These dependencies are used to find the unknown factor, dividend and divisor (when solving equations), as well as to check the results of multiplication and division.
An example of finding the unknown.
x. (- 5) = 10
x = 10: (- 5)
x = - 2
Minus sign in fractions
Divide the number (- 5) by 6 and the number 5 by (- 6).
We remind you that the line is in the recording common fraction- this is the same division sign, and we write the quotient of each of these actions in the form of a negative fraction.
Thus, the minus sign in a fraction can be:
. before a fraction;
. in the numerator;
. in the denominator. 
- When writing negative fractions, the minus sign can be placed in front of the fraction, transferred from the numerator to the denominator, or from the denominator to the numerator.
This is often used when working with fractions, making calculations easier.
Example. Please note that after placing the minus sign in front of the bracket, we subtract the smaller one from the larger module according to the rules for adding numbers with different signs. 
Using the described property of sign transfer in fractions, you can act without finding out which modulus of the data fractional numbers more.
Negative numbers are located to the left of zero. For them, as for positive numbers, an order relation is defined, which allows one to compare one integer with another.
For every natural number n there is one and only one negative number, denoted -n, which complements n to zero: n + (− n) = 0 . Both numbers are called opposite for each other. Subtracting an Integer a is equivalent to adding it with its opposite: -a.
Properties of Negative Numbers
Negative numbers follow almost the same rules as natural numbers, but have some special features.
Historical sketch
Literature
- Vygodsky M. Ya. Handbook of Elementary Mathematics. - M.: AST, 2003. - ISBN 5-17-009554-6
- Glazer G.I. History of mathematics in school. - M.: Education, 1964. - 376 p.
Links
Wikimedia Foundation. 2010.
- Negative landforms
- Negative and positive zero
See what “Negative numbers” are in other dictionaries:
Negative numbers - real numbers, less than zero, for example 2; 0.5; π, etc. See Number... Great Soviet Encyclopedia
Positive and negative numbers- (values). The result of successive additions or subtractions does not depend on the order in which these actions are performed. Eg. 10 5 + 2 = 10 +2 5. Not only the numbers 2 and 5 are rearranged here, but also the signs in front of these numbers. Agreed... ... encyclopedic Dictionary F. Brockhaus and I.A. Efron
numbers are negative- Numbers in accounting that are written in red pencil or red ink. Topics: accounting... Technical Translator's Guide
NEGATIVE NUMBERS- numbers in accounting that are written in red pencil or red ink... Great Accounting Dictionary
Whole numbers- The set of integers is defined as the closure of a set natural numbers regarding the arithmetic operations of addition (+) and subtraction (). Thus, the sum, difference and product of two integers are again integers. It consists of... ... Wikipedia
Integers- numbers that arise naturally when counting (both in the sense of enumeration and in the sense of calculus). There are two approaches to determining natural numbers; numbers used in: listing (numbering) objects (first, second, ... ... Wikipedia
EULER NUMBERS- coefficients E n in the expansion The recurrent formula for E. numbers has the form (in symbolic notation, (E + 1)n + (E 1)n=0, E0 =1. In this case, E 2n+1=0, E4n are positive , E4n+2 negative integers for all n=0, 1, ...; E2= 1, E4=5, E6=61, E8=1385 ... Mathematical Encyclopedia
A negative number- A negative number is an element of the set of negative numbers, which (together with zero) appeared in mathematics when expanding the set of natural numbers. The purpose of the extension is to allow the subtraction operation to be performed on any number. As a result... ... Wikipedia
History of arithmetic- Arithmetic. Painting by Pinturicchio. Apartment Borgia. 1492 1495. Rome, Vatican Palaces ... Wikipedia
Arithmetic- Hans Sebald Beham. Arithmetic. 16th century Arithmetic (ancient Greek ἀ ... Wikipedia
Books
- Mathematics. 5th grade. Educational book and workshop. In 2 parts. Part 2. Positive and negative numbers,. Educational book and a workshop for grade 5 are part of the teaching materials in mathematics for grades 5-6, developed by a team of authors led by E. G. Gelfman and M. A. Kholodnaya within the framework of...
Identifying Positive and Negative Numbers
To determine positive and negative numbers, we use the coordinate line, which is located horizontally and directed from left to right.
Note 1
The origin on the coordinate line corresponds to the number zero, which is neither a positive nor a negative number.
Definition 1
The numbers corresponding to the points of the coordinate line that lie to the right of the origin are called positive.
Definition 2
The numbers corresponding to the points of the coordinate line that lie to the left of the origin are called negative.
From these definitions it follows that the set of all negative numbers is opposite to the set of all positive numbers.
Negative numbers are always written with a “–” (minus) sign.
Example 2
Examples of negative numbers:
- Rational numbers $-\frac(9)(17)$, $-4 \frac(11)(23)$, $–5.25$, $–4,(79)$.
- Irrational numbers$ -\sqrt(2)$, infinite non-periodic decimal fraction $–103.1012341981…$
To simplify writing, positive numbers are often not preceded by a “+” (plus) sign, but negative sign“–” is always written down. In such cases, it is necessary to remember that the entry “$17.4$” is equivalent to the entry “$+17.4$”, the entry “$\sqrt(5)$” is equivalent to the entry “$+\sqrt(5)$”, etc. d.
So the following definition of positive and negative numbers can be used:
Definition 3
Numbers written with a “+” sign are called positive, and with the sign “–” – negative.
The definition of positive and negative numbers is used, which is based on comparison of numbers:
Definition 4
Positive numbers are numbers greater than zero, and negative numbers– numbers less than zero.
Note 3
Thus, the number zero separates positive and negative numbers.
Rules for reading positive and negative numbers
Note 4
When reading a number with a sign in front of it, read its sign first, and then the number itself.
Example 3
For example, “$+17$” is read “plus seventeen”,
“$-3 \frac(4)(11)$” read “minus three point four elevens.”
Note 5
It is worth noting that the names of the plus and minus signs are not declined, while numbers can be declined.
Example 4
Interpretation of positive and negative numbers
Positive numbers are used to denote an increase in some value, arrival, increase, increase in value, etc.
Negative numbers are used for opposite concepts - to indicate a decrease in some value, expense, deficiency, debt, decrease in value, etc.
Let's look at examples.
A reader borrowed $4$ books from the library. Positive value the number $4$ shows the number of books the reader has. If he needs to donate $2$ books to the library, he can use negative meaning$–2$, which will indicate a decrease in the number of books the reader has.
Positive and negative numbers are often used to describe the values of various quantities in measuring instruments. For example, a thermometer for measuring temperature has a scale on which positive and negative values are marked.
Cooling outside by $3$ degrees, i.e. a decrease in temperature can be indicated by a value of $–3$, and an increase in temperature by $5$ degrees can be indicated by a value of $+5$.
It is customary to depict negative numbers in blue, which symbolizes cold, low temperature, and positive numbers are in red, which symbolizes warmth, high temperature. Indicating positive and negative numbers using red and of blue color used in different situations to highlight the sign of numbers.
Now we'll figure it out positive and negative numbers. First, we will give definitions, introduce notation, and then give examples of positive and negative numbers. We will also dwell on the semantic load that positive and negative numbers carry.
Page navigation.
Positive and Negative Numbers - Definitions and Examples
Give identifying positive and negative numbers will help us. For convenience, we will assume that it is located horizontally and directed from left to right.
Definition.
Numbers that correspond to points of the coordinate line lying to the right of the origin are called positive.
Definition.
The numbers that correspond to the points of the coordinate line lying to the left of the origin are called negative.
The number zero, which corresponds to the origin, is neither a positive nor a negative number.
From the definition of negative and positive numbers it follows that the set of all negative numbers is the set of numbers opposite all positive numbers (if necessary, see the article opposite numbers). Therefore, negative numbers are always written with a minus sign.
Now, knowing the definitions of positive and negative numbers, we can easily give examples of positive and negative numbers. Examples of positive numbers are the natural numbers 5, 792 and 101,330, and indeed any natural number is positive. Examples of positive rational numbers are the numbers , 4.67 and 0,(12)=0.121212... , and negative ones are the numbers , −11 , −51.51 and −3,(3) . Examples of positive irrational numbers include the number pi, the number e, and the infinite non-periodic decimal fraction 809.030030003..., and examples of negative irrational numbers are the numbers minus pi, minus e and the number equal to . It should be noted that in the last example it is not at all obvious that the value of the expression is a negative number. To find out for sure, you need to get the value of this expression in the form decimal, and how this is done, we will tell you in the article comparison of real numbers.
Sometimes positive numbers are preceded by a plus sign, just as negative numbers are preceded by a minus sign. In these cases, you should know that +5=5, 
and so on. That is, +5 and 5, etc. - this is the same number, but designated differently. Moreover, you can come across definitions of positive and negative numbers based on the plus or minus sign.
Definition.
Numbers with a plus sign are called positive, and with a minus sign – negative.
There is another definition of positive and negative numbers based on comparison of numbers. To give this definition, it is enough just to remember that the point on the coordinate line corresponding more, lies to the right of the point corresponding to the smaller number.
Definition.
Positive numbers are numbers that are greater than zero, and negative numbers are numbers less than zero.
Thus, zero sort of separates positive numbers from negative ones.
Of course, we should also dwell on the rules for reading positive and negative numbers. If a number is written with a + or − sign, then pronounce the name of the sign, after which the number is pronounced. For example, +8 is read as plus eight, and - as minus one point two fifths. The names of the signs + and − are not declined by case. Example correct pronunciation is the phrase “a equals minus three” (not minus three).
Interpretation of positive and negative numbers
We have been describing positive and negative numbers for quite some time. However, it would be nice to know what meaning they carry? Let's look at this issue.
Positive numbers can be interpreted as an arrival, as an increase, as an increase in some value, and the like. Negative numbers, in turn, mean exactly the opposite - expense, deficiency, debt, reduction of some value, etc. Let's understand this with examples.
We can say that we have 3 items. Here the positive number 3 indicates the number of items we have. How can you interpret the negative number −3? For example, the number −3 could mean that we have to give someone 3 items that we don't even have in stock. Similarly, we can say that at the cash register we were given 3.45 thousand rubles. That is, the number 3.45 is associated with our arrival. In turn, a negative number -3.45 will indicate a decrease in money in the cash register that issued this money to us. That is, −3.45 is the expense. Another example: a temperature increase of 17.3 degrees can be described with a positive number of +17.3, and a temperature decrease of 2.4 can be described with a negative number, as a temperature change of -2.4 degrees.
Positive and negative numbers are often used to describe the values of certain quantities in various measuring instruments. The most accessible example is a device for measuring temperatures - a thermometer - with a scale on which both positive and negative numbers are written. Often negative numbers are depicted in blue (it symbolizes snow, ice, and at temperatures below zero degrees Celsius, water begins to freeze), and positive numbers are written in red (the color of fire, the sun, at temperatures above zero degrees Celsius, ice begins to melt). Writing positive and negative numbers in red and blue is also used in other cases when you need to highlight the sign of the numbers.
Bibliography.
- Vilenkin N.Ya. and others. Mathematics. 6th grade: textbook for general education institutions.
Negative numbers - why do children study something that does not exist?
I am deeply convinced that all (or almost all) problems modern humanity arose as a result of separation from NATURE.
Modern people have become disconnected from nature both physically (with cities and houses) and INTELLECTUALLY.
For example, this is expressed in the fact that almost all school program has nothing to do with nature and REALITY.
I will give just one example - these are the so-called negative numbers.
There is and cannot be anything negative in nature.
Can you imagine minus 1 car? What about minus 3 whites?
A normal, mentally healthy person cannot imagine this!
Almost the only case when we deal with negative quantities is a thermometer. For example, in winter we can see a temperature of -10 degrees Celsius.
But let's see what a thermometer using the Kelvin scale will show us. It will show us approximately 263 degrees Kelvin (instead of -10 Celsius).
What does this mean? This suggests that if you change the calculation scale, negative numbers miraculously turn into positive ones.
I would also like to give a few examples from REAL world, When common sense defeats "negative numbers".
Example No. 1 Measuring the height of mountains, as well as the depths of seas and oceans.
The conventional zero is sea level. Anything higher - they say “so many meters above sea level.” Anything below—we say “so many meters below sea level.”
For example, maximum depth Black Sea = 2,210 meters. Or 2210 meters BELOW sea level. But we do not say that the depth of the sea is (minus) 2210 meters (because this is nonsense).
Example No. 2 Chronography.
Now in European countries It is customary to count years from the Nativity of Christ. This is the basic starting point. Everything that happened after this event is recorded, for example, as 2017 from the Nativity of Christ (or 2017 AD).
Everything that came before this is recorded as “before our era.” For example, egyptian pharaoh lived 1000 BC. Please note that he did not live in minus 1000 years, but 1000 BC. This is an important phrase - “BC” emphasizes the CONVENTIONALITY of the measuring scale.
Those. Historians, praise the spirits, do not have any negative numbers in years!
But mathematicians have cons (negative numbers) and they even teach children how to add, subtract, divide and multiply negative numbers!
Since this phenomenon takes place, it means it is beneficial to someone!
It is clear that this is not beneficial for children. For if you study something that does not exist in nature, it can lead to nervous tension and even to mental disorder.
But who benefits from this? Why are children forced to learn negative numbers?
In search of answers, I turned to Wikipedia (as you know, it never lies). Here's what it says:
A negative number- an element of the set of negative numbers, which (together with zero) appeared in mathematics when expanding the set of natural numbers. The main purpose of the expansion was the desire to make subtraction as valid an operation as addition.
All this is very interesting! But I still didn’t find the answer but my question - “Why is this?”
Ancient Egypt, Babylon and Ancient Greece did not use negative numbers, and if negative roots of equations were obtained (when subtracting), they were rejected as impossible. The exception was Diophantus, who in the 3rd century already knew rule of signs and knew how to multiply negative numbers. However, he considered them only as an intermediate step, useful for calculating the final, positive result.
Yeah, I found the answer to my question:
For the first time, negative numbers were partially legalized in China, and then (from about the 7th century) in India, where they were interpreted as debts (shortages),
