Is 3 an even number or not? Even and odd numbers. The concept of decimal notation of numbers. History and culture

• Odd number- an integer that not shared without remainder: …, −3, −1, 1, 3, 5, 7, 9, …

If m is even, then it can be represented in the form $m\; =\; 2k$, and if odd, then in the form $m\; =\; 2\; k\; +\; 1$, Where $k\; \backslash in\; \backslash mathbb\; Z$.

History and culture

The concept of parity of numbers has been known since ancient times and has often been given a mystical meaning. In Chinese cosmology and natural philosophy, even numbers correspond to the concept of “yin”, and odd numbers correspond to “yang”.

IN different countries There are traditions associated with the number of flowers given. For example in the USA, Europe and some eastern countries It is believed that an even number of flowers given brings happiness. In Russia and the CIS countries, it is customary to bring an even number of flowers only to funerals of the dead. However, in cases where there are many flowers in the bouquet (usually more), the evenness or oddness of their number no longer plays any role. For example, it is quite acceptable to give a lady a bouquet of 12, 14, 16, etc. flowers or sections of a bush flower that have many buds, in which they, in principle, cannot be counted. This is especially true for the larger number of flowers (cuts) given on other occasions.

Practice

In higher educational institutions with complex graphs educational process Even and odd weeks apply. Within these weeks, the schedule of training sessions and, in some cases, their start and end times differ. This practice is used to distribute the load evenly across classrooms, educational buildings and for the rhythm of classes in disciplines with a small classroom load (once every 2 weeks)

Train schedules use even and odd train numbers, depending on the direction of travel (direct or reverse). Accordingly, even/odd denotes the direction in which the train passes through each station.

Even and odd days of the month are sometimes associated with train schedules that are organized every other day.

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Notes

Links

• Sequence A005408 in OEIS: odd numbers
• Sequence A005843 in OEIS: even numbers
• Sequence A179082 in OEIS: even numbers with an even sum of digits in decimal notation

Excerpt describing Even and Odd Numbers

“Well, well,” said Prince Andrei, turning to Alpatych, “tell me everything, as I told you.” - And, without answering a word to Berg, who fell silent next to him, he touched his horse and rode into the alley.

The troops continued to retreat from Smolensk. The enemy followed them. On August 10, the regiment, commanded by Prince Andrei, passed through high road, past the avenue leading to Bald Mountains. The heat and drought lasted for more than three weeks. Every day, curly clouds walked across the sky, occasionally blocking the sun; but in the evening it cleared again, and the sun set in a brownish-red haze. Only heavy dew at night refreshed the earth. The bread that remained on the root burned and spilled out. The swamps are dry. The cattle roared from hunger, not finding food in the sun-burnt meadows. Only at night and in the forests there was still dew and there was coolness. But along the road, along the high road along which the troops marched, even at night, even through the forests, there was no such coolness. The dew was not noticeable on the sandy dust of the road, which had been pushed up more than a quarter of an arshin. As soon as dawn broke, the movement began. The convoys and artillery walked silently along the hub, and the infantry were ankle-deep in soft, stuffy, hot dust that had not cooled down overnight. One part of this sand dust was kneaded by feet and wheels, the other rose and stood as a cloud above the army, sticking into the eyes, hair, ears, nostrils and, most importantly, into the lungs of people and animals moving along this road. The higher the sun rose, the higher the cloud of dust rose, and through this thin, hot dust one could look at the sun, not covered by clouds, with a simple eye. The sun appeared as a large crimson ball. There was no wind, and people were suffocating in this still atmosphere. People walked with scarves tied around their noses and mouths. Arriving at the village, everyone rushed to the wells. They fought for water and drank it until they were dirty.
Prince Andrei commanded the regiment, and the structure of the regiment, the welfare of its people, the need to receive and give orders occupied him. The fire of Smolensk and its abandonment were an era for Prince Andrei. A new feeling of bitterness against the enemy made him forget his grief. He was entirely devoted to the affairs of his regiment, he was caring for his people and officers and affectionate with them. In the regiment they called him our prince, they were proud of him and loved him. But he was kind and meek only with his regimental soldiers, with Timokhin, etc., with completely new people and in a foreign environment, with people who could not know and understand his past; but as soon as he came across one of his former ones, from the staff, he immediately bristled again; he became angry, mocking and contemptuous. Everything that connected his memory with the past repulsed him, and therefore he tried in the relations of this former world only not to be unfair and to fulfill his duty.
True, everything seemed to Prince Andrei in a dark, gloomy light - especially after they left Smolensk (which, according to his concepts, could and should have been defended) on August 6, and after his father, sick, had to flee to Moscow and throw the Bald Mountains, so beloved, built and inhabited by him, for plunder; but, despite this, thanks to the regiment, Prince Andrei could think about another subject completely independent of general issues - about his regiment. On August 10, the column in which his regiment was located reached Bald Mountains. Prince Andrey received news two days ago that his father, son and sister had left for Moscow. Although Prince Andrei had nothing to do in Bald Mountains, he, with his characteristic desire to relieve his grief, decided that he should stop by Bald Mountains.
He ordered a horse to be saddled and from the transition rode on horseback to his father’s village, in which he was born and spent his childhood. Driving past a pond, where dozens of women were always talking, beating rollers and rinsing their laundry, Prince Andrei noticed that there was no one on the pond, and a torn raft, half filled with water, was floating sideways in the middle of the pond. Prince Andrei drove up to the gatehouse. There was no one at the stone entrance gate, and the door was unlocked. The garden paths were already overgrown, and calves and horses were walking around the English park. Prince Andrei drove up to the greenhouse; the glass was broken, and some trees in tubs were knocked down, some withered. He called out to Taras the gardener. Nobody responded. Walking around the greenhouse to the exhibition, he saw that the wooden carved fence was all broken and the plum fruits were torn from their branches. An old man (Prince Andrei saw him at the gate as a child) sat and weaved bast shoes on a green bench.
He was deaf and did not hear Prince Andrei's entrance. He was sitting on a bench where he liked to sit old prince, and near him a sash was hung on the branches of a broken and dried magnolia.
Prince Andrei drove up to the house. Several linden trees in the old garden had been cut down, one piebald horse with a foal walked in front of the house between the rose trees. The house was boarded up with shutters. One window downstairs was open. The yard boy, seeing Prince Andrei, ran into the house.
Alpatych, having sent his family away, remained alone in Bald Mountains; he sat at home and read the Lives. Having learned about the arrival of Prince Andrey, he, with glasses on his nose, buttoned up, left the house, hastily approached the prince and, without saying anything, began to cry, kissing Prince Andrey on the knee.

There are pairs of opposites in the universe, which are an important factor in its structure. The main properties that numerologists attribute to odd (1, 3, 5, 7, 9) and even (2, 4, 6, 8) numbers, as pairs of opposites, are the following:

Odd numbers have much brighter properties. Next to energy “1”, brilliance and luck “3”, adventurous mobility and versatility “5”, wisdom “7” and perfection “9” even numbers don't look as bright. There are 10 main pairs of opposites that exist in the Universe. Among these pairs: even - odd, one - many, right - left, male - female, good - evil. One, right, masculine and good were associated with odd numbers; many, left, feminine and evil - with even ones.

Odd numbers have a certain producing middle, while in any even number there is a perceptive hole, like a lacuna inside itself. The masculine properties of phallic odd numbers arise from the fact that they are stronger than even numbers. If an even number is split in half, then there will be nothing left in the middle except emptiness. It is not easy to break an odd number because there is a dot in the middle. If you combine even and odd numbers together, then the odd one will win, since the result will always be odd. That is why odd numbers have masculine properties, powerful and harsh, while even numbers have feminine, passive and receptive properties. There are an odd number of odd numbers: there are five of them. The even number of even numbers is four.

Odd numbers- solar, electric, acidic and dynamic. They are terms; they are combined with something. Even numbers- lunar, magnetic, alkaline and static. They are deductible, they are reduced. They remain motionless because they have even groups of pairs (2 and 4; 6 and 8).

If we group odd numbers, one number will always be left without its pair (1 and 3; 5 and 7; 9). This makes them dynamic.

Two similar numbers(two odd numbers or two even numbers) are not auspicious.

Even + even = even (static) 2+2=4
even + odd = odd (dynamic) 3+2=5
odd + odd = even (static) 3+3=6

Some numbers are friendly; others oppose each other. The relationships of numbers are determined by the relationships between the planets that rule them. When two friendly numbers touch, their cooperation is not very productive. Like friends, they relax - and nothing happens. But when hostile numbers are in the same combination, they force each other to be on guard and encourage each other to take active action; so these two people work a lot more. In this case, hostile numbers turn out to be actually friends, and friends turn out to be real enemies, slowing down progress. Neutral numbers remain inactive. They do not provide support, do not cause or suppress activity.

Definitions

• Even number- an integer that shares without remainder: ..., −4, −2, 0 , 2, 4, 6, 8, …

• Odd number- an integer that not shared without remainder: …, −3, −1, 1, 3, 5, 7, 9, …

If m is even, then it can be represented in the form m = 2 k (\displaystyle m=2k), and if odd, then in the form m = 2 k + 1 (\displaystyle m=2k+1), Where k ∈ Z (\displaystyle k\in \mathbb (Z) ).

History and culture

The concept of parity of numbers has been known since ancient times and has often been given a mystical meaning. In Chinese cosmology and natural philosophy, even numbers correspond to the concept of “yin”, and odd numbers correspond to “yang”.

In different countries there are traditions related to the number of flowers given. For example, in the USA, Europe and some eastern countries it is believed that an even number of flowers given brings happiness. In Russia and the CIS countries, it is customary to bring an even number of flowers only to funerals of the dead. However, in cases where there are many flowers in the bouquet (usually more), the evenness or oddness of their number no longer plays any role. For example, it is quite acceptable to give a lady a bouquet of 12, 14, 16, etc. flowers or sections of a bush flower that have many buds, in which they, in principle, cannot be counted. This is especially true for the larger number of flowers (cuts) given on other occasions.

Practice

• According to the Traffic Rules, depending on whether the day of the month is even or odd, parking under signs 3.29, 3.30 may be permitted.
• In higher education institutions with complex schedules of the educational process, even and odd weeks are used. Within these weeks, the schedule of training sessions and, in some cases, their start and end times differ. This practice is used to distribute the load evenly across classrooms, academic buildings and to ensure the rhythm of classes in disciplines with a load of 1 time every 2 weeks.
• Even/odd numbers are widely used in railway transport:
  • When a train moves, it is assigned a route number, which can be even or odd depending on the direction of travel (forward or reverse). For example a train "

What do even and odd numbers mean in spiritual numerology. In studying it is very important topic! How are even numbers inherently different from odd numbers?

Even numbers

It is well known that even numbers are those that are divisible by two. That is, the numbers 2, 4, 6, 8, 10, 12, 14, 16, 18 and so on.

What do even numbers mean relative to ? What is the numerological essence of dividing by two? But the point is that all numbers that are divisible by two carry some properties of two.

It has several meanings. Firstly, this is the most “human” number in numerology. That is, the number 2 reflects the whole gamut of human weaknesses, shortcomings and advantages - more precisely, what is generally considered in society to be advantages and disadvantages, “correctness” and “incorrectness”.

And since these labels of “correctness” and “incorrectness” reflect our limited views of the world, then two has the right to be considered the most limited, the most “stupid” number in numerology. From this it is clear that even numbers are much more “hard-headed” and straightforward than their odd counterparts, which are not divisible by two.

This, however, does not mean that even numbers are worse than odd numbers. They are simply different and reflect other forms of human existence and consciousness in comparison with odd numbers. Even numbers in spiritual numerology always obey the laws of ordinary, material, “earthly” logic. Why?

Because another meaning of two: standard logical thinking. And all even numbers in spiritual numerology, one way or another, are subject to certain logical rules for the perception of reality.

An elementary example: if a stone is thrown up, it, having gained a certain height, then rushes to the ground. This is how even numbers “think”. And odd numbers would easily suggest that the stone would fly off into space; or it won’t make it, but will get stuck somewhere in the air... for a long time, for centuries. Or it will just dissolve! The more illogical the hypothesis, the closer it is to odd numbers.

Odd numbers

Odd numbers are those that are not divisible by two: the numbers 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21 and so on. From the perspective of spiritual numerology, odd numbers are subject not to material, but to spiritual logic.

Which, by the way, gives food for thought: why is the number of flowers in a bouquet for a living person odd, but even for a dead person... Is it because material logic (logic within the “yes-no” framework) is dead relative to the human soul?

Visible coincidences of material logic and spiritual logic occur very often. But don't let this fool you. The logic of the spirit, that is, the logic of odd numbers, is never fully traceable on the external, physical levels of human existence and consciousness.

Let's take for example the number of love. We talk about love at every turn. We confess to it, dream about it, decorate our lives and the lives of others with it.

But what do we really know about love? About that all-pervading Love that permeates all spheres of the Universe. How can we agree and accept that there is as much cold as warmth, as much hatred as kindness?! Are we able to realize that it is these paradoxes that constitute the highest, creative essence of Love?!

Paradoxicality is one of the key properties of odd numbers. IN interpretation of odd numbers we must understand: what seems to a person does not always really exist. But at the same time, if something seems to someone, then it already exists. There are different levels of Existence, and illusion is one of them...

By the way, mental maturity is characterized by the ability to perceive paradoxes. Therefore, it takes a little more brainpower to explain odd numbers than it does to explain even numbers.

Even and odd numbers in numerology

Let's summarize. What is the main difference between even numbers and odd numbers?

Even numbers are more predictable (except for the number 10), solid and consistent. Events and people associated with even numbers are more stable and explainable. Quite available for external changes, but only for external ones! Internal changes are the area of ​​odd numbers...

Odd numbers are eccentric, freedom-loving, unstable, unpredictable. They always bring surprises. You seem to know the meaning of some odd number, but it, this number, suddenly begins to behave in such a way that it makes you reconsider almost your entire life...

Note!

My book entitled “Spiritual Numerology” has already arrived in stores. The language of numbers." Today, this is the most complete and popular of all existing esoteric manuals on the meaning of numbers. More about this,and also to order the book, follow the following link: « «

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There are pairs of opposites in the universe, which are an important factor in its structure. The main properties that numerologists attribute to even (1, 3, 5, 7, 9) and odd (2, 4, 6, 8) numbers, as pairs of opposites, are the following:

1 - active, purposeful, domineering, callous, leadership, initiative;
2 - passive, receptive, weak, sympathetic, subordinate;
3 - bright, cheerful, artistic, lucky, easily achieving success;
4 - hardworking, boring, lack of initiative, unhappy, hard work and frequent defeat;
5 - active, enterprising, nervous, insecure, sexy;
6 - simple, calm, homely, settled; mother's love;
7 - withdrawal from the world, mysticism, secrets;
8 - worldly life; material success or failure;
9 - intellectual and spiritual perfection.

Odd numbers have much more striking properties. Next to the energy of “1”, the brilliance and luck of “3”, the adventurous mobility and versatility of “5”, the wisdom of “7” and the perfection of “9”, even numbers do not look so bright. There are 10 main pairs of opposites that exist in the Universe. Among these pairs: even - odd, one - many, right - left, male - female, good - evil. One, right, masculine and good were associated with odd numbers; many, left, feminine and evil - with even ones.

Odd numbers have a certain generating middle, while in any even number there is a perceptive hole, like a lacuna inside itself. The masculine properties of phallic odd numbers arise from the fact that they are stronger than even numbers. If an even number is split in half, then there will be nothing left in the middle except emptiness. It is not easy to break an odd number because there is a dot in the middle. If you combine even and odd numbers together, then the odd one will win, since the result will always be odd. That is why odd numbers have masculine properties, powerful and harsh, while even numbers have feminine, passive and receptive properties.

There are an odd number of odd numbers: there are five of them. The even number of even numbers is four.

Odd numbers are solar, electric, acidic and dynamic. They are terms; they are combined with something. Even numbers are lunar, magnetic, alkaline and static. They are deductible, they are reduced. They remain motionless because they have even groups of pairs (2 and 4; 6 and 8).

If we group odd numbers, one number will always be left without its pair (1 and 3; 5 and 7; 9). This makes them dynamic. Two similar numbers (two odd numbers or two even numbers) are not favorable.

even + even = even (static) 2+2=4
even + odd = odd (dynamic) 3+2=5
odd + odd = even (static) 3+3=6

Some numbers are friendly, others are opposed to each other. The relationships between numbers are determined by the relationships between the planets that rule them (details in the “Number Compatibility” section). When two friendly numbers touch, their cooperation is not very productive. Like friends, they relax - and nothing happens. But when hostile numbers are in the same combination, they force each other to be on guard and encourage each other to take active action; so these two people work a lot more. In this case, hostile numbers turn out to be actually friends, and friends turn out to be real enemies, slowing down progress. Neutral numbers remain inactive. They do not provide support, do not cause or suppress activity.