Integers for short. Whole numbers. Definition

The information in this article forms general idea O integers. First, a definition of integers is given and examples are given. Next, we consider integers on the number line, from where it becomes clear which numbers are called positive integers and which are called negative integers. After this, it is shown how changes in quantities are described using integers, and negative integers are considered in the sense of debt.

Page navigation.

Integers - Definition and Examples

Definition.

Whole numbers– these are natural numbers, the number zero, as well as numbers opposite to the natural ones.

The definition of integers states that any of the numbers 1, 2, 3, …, the number 0, as well as any of the numbers −1, −2, −3, … is an integer. Now we can easily bring examples of integers. For example, the number 38 is an integer, the number 70,040 is also an integer, zero is an integer (remember that zero is NOT a natural number, zero is an integer), the numbers −999, −1, −8,934,832 are also examples of integers numbers.

It is convenient to represent all integers as a sequence of integers that has next view: 0, ±1, ±2, ±3, … The sequence of integers can be written like this: …, −3, −2, −1, 0, 1, 2, 3, …

From the definition of integers it follows that the set of natural numbers is a subset of the set of integers. Therefore, every natural number is an integer, but not every integer is a natural number.

Integers on a coordinate line

Definition.

Positive integers are integers greater than zero.

Definition.

Negative integers are integers that are less than zero.

Positive and negative integers can also be determined by their position on the coordinate line. On a horizontal coordinate line, points whose coordinates are positive integers lie to the right of the origin. In turn, points with negative integer coordinates are located to the left of point O.

It is clear that the set of all positive integers is the set of natural numbers. In turn, the set of all negative integers is the set of all numbers opposite to the natural numbers.

Separately, let us draw your attention to the fact that we can safely call any natural number an integer, but we cannot call any integer a natural number. We can call natural only any whole positive number, since negative integers and zero are not natural numbers.

Non-positive and non-negative integers

Let us give definitions of non-positive integers and non-negative integers.

Definition.

All positive integers, together with the number zero, are called non-negative integers.

Definition.

Non-positive integers– these are all negative integers together with the number 0.

In other words, the whole is not a negative number is an integer that is greater than zero or equal to zero, and a non-positive integer is an integer that is less than zero or equal to zero.

Examples of non-positive integers are the numbers −511, −10,030, 0, −2, and as examples of non-negative integers we give the numbers 45, 506, 0, 900,321.

Most often, the terms “non-positive integers” and “non-negative integers” are used for brevity. For example, instead of the phrase “the number a is an integer, and a is greater than zero or equal to zero,” you can say “a is a non-negative integer.”

Describing changes in quantities using integers

It's time to talk about why integers are needed in the first place.

The main purpose of integers is that with their help it is convenient to describe changes in the quantity of any objects. Let's understand this with examples.

Let there be a certain number of parts in the warehouse. If, for example, 400 more parts are brought to the warehouse, then the number of parts in the warehouse will increase, and the number 400 expresses this change in quantity in positive side(increasing). If, for example, 100 parts are taken from the warehouse, then the number of parts in the warehouse will decrease, and the number 100 will express a change in quantity in the negative direction (downwards). Parts will not be brought to the warehouse, and parts will not be taken away from the warehouse, then we can talk about the constant quantity of parts (that is, we can talk about zero change in quantity).

In the examples given, the change in the number of parts can be described using the integers 400, −100 and 0, respectively. A positive integer 400 indicates a change in quantity in a positive direction (increase). A negative integer −100 expresses a change in quantity in a negative direction (decrease). The integer 0 indicates that the quantity remains unchanged.

The convenience of using integers compared to using natural numbers is that you do not have to explicitly indicate whether the quantity is increasing or decreasing - the integer quantifies the change, and the sign of the integer indicates the direction of the change.

Integers can also express not only a change in quantity, but also a change in some quantity. Let's understand this using the example of temperature changes.

A rise in temperature of, say, 4 degrees is expressed as a positive integer 4. A decrease in temperature, for example, by 12 degrees can be described by a negative integer −12. And the invariance of temperature is its change, determined by the integer 0.

Separately, it is necessary to say about the interpretation of negative integers as the amount of debt. For example, if we have 3 apples, then the positive integer 3 represents the number of apples we own. On the other hand, if we have to give 5 apples to someone, but we don’t have them in stock, then this situation can be described using a negative integer −5. In this case, we “own” −5 apples, the minus sign indicates debt, and the number 5 quantifies debt.

Understanding a negative integer as a debt allows, for example, to justify the rule for adding negative integers. Let's give an example. If someone owes 2 apples to one person and 1 apple to another, then the total debt is 2+1=3 apples, so −2+(−1)=−3.

Bibliography.

• Vilenkin N.Ya. and others. Mathematics. 6th grade: textbook for general education institutions.

A bunch of is a set of any objects that are called elements of this set.

For example: many schoolchildren, many cars, many numbers .

In mathematics, set is considered much more broadly. We will not delve too deeply into this topic, since it relates to higher mathematics and may create learning difficulties at first. We will consider only that part of the topic that we have already dealt with.

Designations

A set is most often denoted by capital letters of the Latin alphabet, and its elements by lowercase letters. In this case, the elements are enclosed in curly braces.

For example, if our friends name is Tom, John and Leo , then we can define a set of friends whose elements will be Tom, John and Leo.

Let's denote many of our friends using a capital Latin letter F(friends), then put an equal sign and list our friends in curly brackets:

F = (Tom, John, Leo)

Example 2. Let's write down the set of divisors of the number 6.

Let us denote this set by any capital Latin letter, for example, by the letter D

then we put an equal sign and list the elements of this set in curly brackets, that is, we list the divisors of the number 6

D = (1, 2, 3, 6)

If some element belongs to a given set, then this membership is indicated using the membership sign ∈. For example, the divisor 2 belongs to the set of divisors of the number 6 (the set D). It is written like this:

Reads like: “2 belongs to the set of divisors of the number 6”

If some element does not belong to a given set, then this non-membership is indicated using a crossed out membership sign ∉. For example, the divisor 5 does not belong to the set D. It is written like this:

Reads like: "5 do not belong set of divisors of the number 6″

In addition, a set can be written by directly listing the elements, without capital letters. This can be convenient if the set consists of a small number of elements. For example, let's define a set of one element. Let this element be our friend Volume:

( Volume )

Let's define a set that consists of one number 2

{ 2 }

Let's define a set that consists of two numbers: 2 and 5

{ 2, 5 }

Set of natural numbers

This is the first set we started working with. Natural numbers are the numbers 1, 2, 3, etc.

Integers appeared because of the need of people to count those other objects. For example, count the number of chickens, cows, horses. Natural numbers arise naturally when counting.

In previous lessons, when we used the word "number", most often it was a natural number that was meant.

In mathematics, the set of natural numbers is denoted by a capital letter N.

For example, let's point out that the number 1 belongs to the set of natural numbers. To do this, we write down the number 1, then using the membership sign ∈ we indicate that the unit belongs to the set N

1 ∈ N

Reads like: “one belongs to the set of natural numbers”

Set of integers

The set of integers includes all positive and , as well as the number 0.

A set of integers is denoted by a capital letter Z .

Let us point out, for example, that the number −5 belongs to the set of integers:

−5 ∈ Z

Let us point out that 10 belongs to the set of integers:

10 ∈ Z

Let us point out that 0 belongs to the set of integers:

In the future, we will call all positive and negative numbers one phrase - whole numbers.

Set of rational numbers

Rational numbers are the same ordinary fractions that we study to this day.

A rational number is a number that can be represented as a fraction, where a- numerator of the fraction, b- denominator.

The numerator and denominator can be any numbers, including integers (with the exception of zero, since you cannot divide by zero).

For example, imagine that instead of a is the number 10, but instead b- number 2

10 divided by 2 equals 5. We see that the number 5 can be represented as a fraction, which means the number 5 is included in the set rational numbers.

It is easy to see that the number 5 also applies to the set of integers. Therefore, the set of integers is included in the set of rational numbers. This means that the set of rational numbers includes not only ordinary fractions, but also integers of the form −2, −1, 0, 1, 2.

Now let's imagine that instead of a the number is 12, but instead b- number 5.

12 divided by 5 equals 2.4. We see that decimal 2.4 can be represented as a fraction, which means it is included in the set of rational numbers. From this we conclude that the set of rational numbers includes not only ordinary fractions and integers, but also decimal fractions.

We calculated the fraction and got the answer 2.4. But we could isolate the whole part of this fraction:

When isolating the whole part in a fraction, it turns out mixed number. We see that a mixed number can also be represented as a fraction. This means that the set of rational numbers also includes mixed numbers.

As a result, we come to the conclusion that the set of rational numbers contains:

• whole numbers
• common fractions
• decimals
• mixed numbers

The set of rational numbers is denoted by a capital letter Q.

For example, we point out that a fraction belongs to the set of rational numbers. To do this, we write down the fraction itself, then using the membership sign ∈ we indicate that the fraction belongs to the set of rational numbers:

∈ Q

Let us point out that the decimal fraction 4.5 belongs to the set of rational numbers:

4,5 ∈ Q

Let us point out that a mixed number belongs to the set of rational numbers:

∈ Q

The introductory lesson on sets is complete. We'll look at sets much better in the future, but for now what's covered in this lesson will suffice.

Did you like the lesson?
Join our new group VKontakte and start receiving notifications about new lessons

Let's say Achilles runs ten times faster than the tortoise and is a thousand steps behind it. During the time it takes Achilles to run this distance, the tortoise will crawl a hundred steps in the same direction. When Achilles runs a hundred steps, the tortoise crawls another ten steps, and so on. The process will continue ad infinitum, Achilles will never catch up with the tortoise.

This reasoning became a logical shock for all subsequent generations. Aristotle, Diogenes, Kant, Hegel, Hilbert... They all considered Zeno's aporia in one way or another. The shock was so strong that " ... discussions continue to this day; the scientific community has not yet been able to come to a common opinion on the essence of paradoxes ... mathematical analysis, set theory, new physical and philosophical approaches were involved in the study of the issue; none of them became a generally accepted solution to the problem..."[Wikipedia, "Zeno's Aporia". Everyone understands that they are being fooled, but no one understands what the deception consists of.

From a mathematical point of view, Zeno in his aporia clearly demonstrated the transition from quantity to . This transition implies application instead of permanent ones. As far as I understand, the mathematical apparatus for using variable units of measurement has either not yet been developed, or it has not been applied to Zeno’s aporia. Applying our usual logic leads us into a trap. We, due to the inertia of thinking, apply constant units of time to the reciprocal value. From a physical point of view, this looks like time slowing down until it stops completely at the moment when Achilles catches up with the turtle. If time stops, Achilles can no longer outrun the tortoise.

If we turn our usual logic around, everything falls into place. Achilles runs with constant speed. Each subsequent segment of his path is ten times shorter than the previous one. Accordingly, the time spent on overcoming it is ten times less than the previous one. If we apply the concept of “infinity” in this situation, then it would be correct to say “Achilles will catch up with the turtle infinitely quickly.”

How to avoid this logical trap? Remain in constant units of time and do not switch to reciprocal units. In Zeno's language it looks like this:

In the time it takes Achilles to run a thousand steps, the tortoise will crawl a hundred steps in the same direction. During the next time interval equal to the first, Achilles will run another thousand steps, and the tortoise will crawl a hundred steps. Now Achilles is eight hundred steps ahead of the tortoise.

This approach adequately describes reality without any logical paradoxes. But it is not complete solution Problems. Einstein’s statement about the irresistibility of the speed of light is very similar to Zeno’s aporia “Achilles and the Tortoise”. We still have to study, rethink and solve this problem. And the solution must be sought not in infinitely large numbers, but in units of measurement.

Another interesting aporia of Zeno tells about a flying arrow:

A flying arrow is motionless, since at every moment of time it is at rest, and since it is at rest at every moment of time, it is always at rest.

In this aporia, the logical paradox is overcome very simply - it is enough to clarify that at each moment of time a flying arrow is at rest at different points in space, which, in fact, is motion. Another point needs to be noted here. From one photograph of a car on the road it is impossible to determine either the fact of its movement or the distance to it. To determine whether a car is moving, you need two photographs taken from the same point in different moments time, but distance cannot be determined from them. To determine the distance to a car, you need two photographs taken from different points in space at one point in time, but from them you cannot determine the fact of movement (of course, you still need additional data for calculations, trigonometry will help you). What I want to point out Special attention, is that two points in time and two points in space are different things that should not be confused, because they provide different opportunities for research.

Wednesday, July 4, 2018

The differences between set and multiset are described very well on Wikipedia. Let's see.

As you can see, “there cannot be two identical elements in a set,” but if there are identical elements in a set, such a set is called a “multiset.” Reasonable beings will never understand such absurd logic. This is the level talking parrots and trained monkeys, who have no intelligence from the word “completely”. Mathematicians act as ordinary trainers, preaching to us their absurd ideas.

Once upon a time, the engineers who built the bridge were in a boat under the bridge while testing the bridge. If the bridge collapsed, the mediocre engineer died under the rubble of his creation. If the bridge could withstand the load, the talented engineer built other bridges.

No matter how mathematicians hide behind the phrase “screw me, I’m in the house”, or rather “mathematics studies abstract concepts", there is one umbilical cord that inextricably connects them with reality. This umbilical cord is money. Apply mathematical theory sets to the mathematicians themselves.

We studied mathematics very well and now we are sitting at the cash register, giving out salaries. So a mathematician comes to us for his money. We count out the entire amount to him and lay it out on our table in different piles, into which we put bills of the same denomination. Then we take one bill from each pile and give the mathematician his “mathematical set of salary.” Let us explain to the mathematician that he will receive the remaining bills only when he proves that a set without identical elements is not equal to a set with identical elements. This is where the fun begins.

First of all, the logic of the deputies will work: “This can be applied to others, but not to me!” Then they will begin to reassure us that bills of the same denomination have different bill numbers, which means they cannot be considered the same elements. Okay, let's count salaries in coins - there are no numbers on the coins. Here the mathematician will begin to frantically remember physics: on different coins there is different quantities dirt, crystal structure and atomic arrangement of each coin is unique...

And now I have the most interest Ask: where is the line beyond which the elements of a multiset turn into elements of a set and vice versa? Such a line does not exist - everything is decided by shamans, science is not even close to lying here.

Look here. We select football stadiums with the same field area. The areas of the fields are the same - which means we have a multiset. But if we look at the names of these same stadiums, we get many, because the names are different. As you can see, the same set of elements is both a set and a multiset. Which is correct? And here the mathematician-shaman-sharpist pulls out an ace of trumps from his sleeve and begins to tell us either about a set or a multiset. In any case, he will convince us that he is right.

To understand how modern shamans operate with set theory, tying it to reality, it is enough to answer one question: how do the elements of one set differ from the elements of another set? I'll show you, without any "conceivable as not a single whole" or "not conceivable as a single whole."

Sunday, March 18, 2018

The sum of the digits of a number is a dance of shamans with a tambourine, which has nothing to do with mathematics. Yes, in mathematics lessons we are taught to find the sum of the digits of a number and use it, but that’s why they are shamans, to teach their descendants their skills and wisdom, otherwise shamans will simply die out.

Do you need proof? Open Wikipedia and try to find the page "Sum of digits of a number." She doesn't exist. There is no formula in mathematics that can be used to find the sum of the digits of any number. After all, numbers are graphic symbols with which we write numbers, and in the language of mathematics the task sounds like this: “Find the sum of graphic symbols representing any number.” Mathematicians cannot solve this problem, but shamans can do it easily.

Let's figure out what and how we do in order to find the sum of the digits of a given number. And so, let us have the number 12345. What needs to be done in order to find the sum of the digits of this number? Let's consider all the steps in order.

1. Write down the number on a piece of paper. What have we done? We have converted the number into a graphical number symbol. This is not a mathematical operation.

2. We cut one resulting picture into several pictures containing individual numbers. Cutting a picture is not a mathematical operation.

3. Convert individual graphic symbols into numbers. This is not a mathematical operation.

4. Add the resulting numbers. Now this is mathematics.

The sum of the digits of the number 12345 is 15. These are the “cutting and sewing courses” taught by shamans that mathematicians use. But that is not all.

From a mathematical point of view, it does not matter in which number system we write a number. So, in different systems In calculus, the sum of the digits of the same number will be different. In mathematics, the number system is indicated as a subscript to the right of the number. With the large number 12345, I don’t want to fool my head, let’s consider the number 26 from the article about. Let's write this number in binary, octal, decimal and hexadecimal number systems. We won't look at every step under a microscope; we've already done that. Let's look at the result.

As you can see, in different number systems the sum of the digits of the same number is different. This result has nothing to do with mathematics. It’s the same as if you determined the area of ​​a rectangle in meters and centimeters, you would get completely different results.

Zero looks the same in all number systems and has no sum of digits. This is another argument in favor of the fact that. Question for mathematicians: how is something that is not a number designated in mathematics? What, for mathematicians nothing exists except numbers? I can allow this for shamans, but not for scientists. Reality is not just about numbers.

The result obtained should be considered as proof that number systems are units of measurement for numbers. After all, we cannot compare numbers with different units of measurement. If the same actions with different units of measurement of the same quantity lead to different results after comparing them, it means it has nothing to do with mathematics.

What is real mathematics? This is when the result of a mathematical operation does not depend on the size of the number, the unit of measurement used and on who performs this action.

Oh! Isn't this the women's restroom?
- Young woman! This is a laboratory for the study of the indephilic holiness of souls during their ascension to heaven! Halo on top and arrow up. What other toilet?

Female... The halo on top and the arrow down are male.

If something like this flashes before your eyes several times a day design art,

Then it’s not surprising that you suddenly find a strange icon in your car:

Personally, I make an effort to see minus four degrees in a pooping person (one picture) (a composition of several pictures: a minus sign, the number four, a designation of degrees). And I don’t think this girl is a fool who doesn’t know physics. She just has a strong stereotype of perceiving graphic images. And mathematicians teach us this all the time. Here's an example.

1A is not “minus four degrees” or “one a”. This is "pooping man" or the number "twenty-six" in hexadecimal notation. Those people who constantly work in this number system automatically perceive a number and a letter as one graphic symbol.

TO integers include natural numbers, zero, and numbers opposite to natural numbers.

Integers are positive integers.

For example: 1, 3, 7, 19, 23, etc. We use such numbers for counting (there are 5 apples on the table, a car has 4 wheels, etc.)

Latin letter \mathbb(N) - denoted set of natural numbers.

Natural numbers cannot include negative numbers (a chair cannot have a negative number of legs) and fractional numbers (Ivan could not sell 3.5 bicycles).

The opposite of natural numbers are negative integers: −8, −148, −981, ….

Arithmetic operations with integers

What can you do with integers? They can be multiplied, added and subtracted from each other. Let's look at each operation using a specific example.

Addition of integers

Two integers with identical signs are added up as follows: the modules of these numbers are added and the resulting sum is preceded by a final sign:

(+11) + (+9) = +20

Subtracting Integers

Two integers with different signs are added up as follows: the modulus of the smaller one is subtracted from the modulus of the larger number and the sign of the larger modulo of the number is placed in front of the resulting answer:

(-7) + (+8) = +1

Multiplying Integers

To multiply one integer by another, you need to multiply the moduli of these numbers and put a “+” sign in front of the resulting answer if the original numbers had the same signs, and a “−” sign if the original numbers had different signs:

(-5)\cdot (+3) = -15

(-3)\cdot (-4) = +12

The following should be remembered rule for multiplying integers:

+ \cdot + = +

+ \cdot - = -

- \cdot + = -

- \cdot - = +

There is a rule for multiplying multiple integers. Let's remember it:

The sign of the product will be “+” if the number of factors with a negative sign is even and “−” if the number of factors with a negative sign is odd.

(-5) \cdot (-4) \cdot (+1) \cdot (+6) \cdot (+1) = +120

Integer division

The division of two integers is carried out as follows: the modulus of one number is divided by the modulus of the other, and if the signs of the numbers are the same, then the sign “+” is placed in front of the resulting quotient, and if the signs of the original numbers are different, then the sign “−” is placed.

(-25) : (+5) = -5

Properties of addition and multiplication of integers

Let's look at the basic properties of addition and multiplication for any integers a, b and c:

1. a + b = b + a - commutative property of addition;
2. (a + b) + c = a + (b + c) - combinative property of addition;
3. a \cdot b = b \cdot a - commutative property of multiplication;
4. (a \cdot c) \cdot b = a \cdot (b \cdot c)- associative properties of multiplication;
5. a \cdot (b \cdot c) = a \cdot b + a \cdot c- distributive property of multiplication.

Teacher of the highest category

What numbers are called integers?

Lesson objectives:

-Expand the concept of number by introducing negative numbers:

-Develop the skill of writing positive and negative numbers.

Lesson objectives.

Educational – promote the development of the ability to generalize and systematize, promote the development of mathematical horizons, thinking and speech, attention and memory.

Educational – fostering an attitude towards self-education, self-education, precise performance, a creative attitude to activity, critical thinking.

Developmental – develop in schoolchildren the ability to compare and generalize, logically express thoughts, develop mathematical horizons, thinking and speech, attention and memory.

During the classes:

1. Introductory conversation.

So far in mathematics lessons we have looked at what numbers?

-Natural and fractional.

What numbers are called natural numbers?

- These are numbers used when counting objects.

How many can you say?

- infinitely many.

Is zero a natural number? Why?

-What are fractional numbers used for?

-We not only count objects, but parts of certain quantities.

What fractions do you know?

- Ordinary and decimal.

Task No. 1.

Among the numbers, what are the natural numbers? Common fractions? Decimals?

10; 1,1; https://pandia.ru/text/77/504/images/image002_2.png" width="16" height="35 src="> ; https://pandia.ru/text/77/504/images/image004_0.png" width="24" height="35 src="> .

2. Explanation of new material:

However, in your life you have probably already encountered other numbers, which ones? Where?

-Negative. For example, in a weather report.

Before you start studying new topic, let's discuss signs that will help in expanding the set of numbers. These are plus and minus signs. Think about what these signs are associated with in life. It can be anything: white - black, good - bad. We will write your examples in the form of a table.

Just two signs evoke so many thoughts. In fact, these two signs provide the opportunity to go in different directions. Such numbers, “similar” to natural numbers, but with a minus sign, are needed in cases where a quantity can change in two opposite directions. To express a value as a negative number, some initial, zero mark is introduced. Let's look at the examples that others have done, and at home you can think about it and make your own presentation. Slide No. 2-7.

Using the sign is very convenient. Its use is accepted throughout the world. But it was not always so. Slide number 8.

So, along with the natural numbers

1, 2, 3, 4, 5, …100, …, 1000, …

We will consider negative numbers, each of which is obtained by adding a minus sign to the corresponding natural number:

-1,- 2, - 3, - 4, - 5, …-100, …,- 1000, …

A natural number and its corresponding negative number are called opposites. For example, the numbers 15 and -15. You can use -15 and 15. O is the opposite of itself.

Rule: Natural numbers, their negative opposites and the number 0 are called whole numbers. All these numbers together make up the set of integers.

Open the textbook, page 159, find the rule, read it again, and learn it by heart at home.

A natural number is also commonly called a positive integer, that is, it is the same thing. In front of him, in order to emphasize external difference from negative, sometimes a plus sign is added. +5=5.

3. Formation of skills and abilities:

1) № 000.

2) Write these numbers into two groups: positive and negative:

-15, 7, 28, -41, 0, 382, -591, -999, 2000.

3) Game “my mood”.

Now you will rate your mood at the moment on the following scale:

Good mood: +1, +2, +3, +4, +5.

Bad mood: -1, -2, -3, -4, -5.

One person will write the results on the board, and everyone else will take turns saying out loud: “I have good mood by 4 points"

4) Game "cracker"

I will name pairs of numbers, if the pair is opposite, then you clap your hands, if not, then there should be silence in the class:

5 and -5; 6 and 0.6; -300 and 300; 3 and 1/3; 8 and 80; 14 and -14; 5/7 and 7/5; -1 and 1.

5) Propaedeutics for learning the addition of integers:

No. 000 (a).

We look at the solution using the presentation. Slide number 8.

4. Lesson summary:

-What numbers are called positive? Negative?

-What did you find out about O?

- What are negative numbers used for?

-How are positive and negative numbers written?

5. D/Z: clause 8.1, No. 000, 721(b), 715(b). Creative task: write a poem about whole numbers, a drawing, a presentation, a fairy tale.

We will subtract another from the number,
We put a straight line.
We recognize this sign
“Minus” we call him.
1.
Worth one
Looks like a match.
She's just a devil
With a small bang.

2.
It barely glides through the water,
Like a swan, number two.
She arched her neck,
Drives the waves behind him.

3.
Two hooks, look
The result was number three.
But these two hooks
You can't get a worm.

4.
Somehow the fork was dropped
One clove was broken off.
This fork is in the whole world
It's called "four".

5.
Number five - with a big belly,
Wears a cap with a visor.
At school this number is five
Children love to receive.

6.
What a cherry, my friend,
Is the stem bent upward?
Try to eat it
This cherry is number six.

7.
I'm such a poker
I can't put it in the oven.
Everyone knows about her
That it's called "seven".

8.
The rope was twisting, twisting,
Braided into two loops.
"What is this number?" - Let's ask mom.
Mom will answer us: “Eight.”

9.
The wind blew and blew strong,
He turned the cherry over.
Number six, please tell me
It turned into the number nine.

10.
Like an older sister
The zero is led by one.
We just walked together
They immediately became the number ten.

Poems about mathematics

· Much of mathematics does not remain in memory, but when you understand it, then it is easy to remember what you have forgotten on occasion.