What is an even number? Odd and even
The mysterious influence of numbers that surround us has been known since ancient times. Each number has its own special meaning and has its own impact. And dividing numbers into even and odd is very important for determining our future destiny.
Even and odd
In numerology (the science of the connections between numbers and people’s lives), odd numbers (1, 3, 5, 7, 9, 11, and so on) are considered exponents of the masculine principle, which in Eastern philosophy is called yang. They are also called solar because they carry the energy of our star. Such numbers reflect a search, a desire for something new.Even numbers (which are divisible by 2 without a remainder) speak about feminine nature (in Eastern philosophy - yin) and the energy of the Moon. Their essence is that they initially gravitate towards two, since they are divided into it. These numbers indicate a desire for logical rules for displaying reality and a reluctance to go beyond them.
In other words: even numbers are more correct, but at the same time more limited and straightforward. And the odd ones can help you get out of a boring and gray existence.
There are more odd numbers (zero in numerology has its own meaning and is not considered an even number) - five (1, 3, 5, 7, 9) versus four (2,4,6, 8). There are more of them strong energy is expressed in the fact that when they are added to even numbers, an odd number is again obtained.
The contrast between even and odd numbers is included in common system opposites (one - many, man - woman, day - night, right - left, good - evil, etc.). Moreover, the first concepts are associated with odd numbers, and the second ones with even numbers.
Thus, any odd number has masculine characteristics: authority, harshness, the ability to perceive something new, and any even number is endowed with feminine properties: passivity, the desire to smooth out any conflict.
Meanings of numbers
All numbers in numerology have certain meanings: One carries activity, determination, initiative. Two - receptivity, weakness, willingness to obey. Three - fun, artistry, luck. Four - hard work, monotony, boredom, obscurity, defeat. Five - entrepreneurship, success in love, movement towards a goal. Six - simplicity, calmness, attraction to home comfort. Seven - mysticism, mystery. Eight - material wealth. Nine - intellectual and spiritual perfection, high achievements. As you can see, odd numbers have much brighter properties. According to the teachings of the famous ancient Greek mathematician Pythagoras, they were the personification of goodness, life and light, and also symbolized the right side of man - the side of luck.Even numbers were associated with the unlucky left side, evil, darkness and death. These views of the Pythagoreans were later reflected in some superstitions (for example, that it is impossible to give an even number of flowers to a living person or that standing with the left foot means a bad day), although different nations they may be different.
The influence of even and odd numbers on our lives
Since the time of Pythagoras, it has been generally accepted that “female” even numbers are associated with evil because they are easily split into two halves - and this means that we can say that inside them there is empty space, primitive chaos. But an odd number cannot be split into equal parts without a remainder; therefore, it contains within itself something whole and even sacred (in the Middle Ages, some theological philosophers argued that God lives inside odd numbers).In modern numerology, it is customary to take into account many numbers around us - for example, telephone or apartment numbers, dates of birth and significant events, numbers of first and last names, etc.
The most important for our lives is the so-called destiny number, which is calculated by date of birth. You need to add up all the numbers of this date and “collapse” them to a simple number.
Let's say you were born on September 28, 1968 (09/28/1968). Add the numbers: 2+8+0+9+1+9+ 6 -I- 8 = 43; 4 + 3 = 7. Therefore, your destiny number is 7 (as mentioned above, the number of mysticism and mystery).
In the same way, you can analyze the dates of events that are important to you. In this regard, the fate of the famous Napoleon is very indicative. He was born on August 15, 1769 (08/15/1769), therefore, his destiny number is equal to one:
1 + 5 + 0 + 8 + 1 + 7 + 6 + 9 = 37; 3 + 7 = 10; 1 + 0 = 1.
This odd number, according to modern numerology, carries activity, determination, initiative - qualities thanks to which Napoleon showed himself. He became the French Emperor on December 2, 1804 (12/02/1804), the number of this date is nine (0 + 2 + 1 + 2 + 1 + 8 + 0 + 4 = 18; 1 + 8 = 9), which is the number of high achievements . He died on May 5, 1821 (05/05/1821), the number of this day is four (0 + 5 + 0 + 5 + 1+ 8 + 2 + 1 = 22; 2 + 2 = 4), which means obscurity and defeat.
It was not for nothing that ancient people said that numbers rule the world. Using the knowledge of numerology, you can easily calculate what events a particular date promises - and in which cases you should refrain from unnecessary actions.
What do even and odd numbers mean in spiritual numerology. This is a very important topic in learning the language of numbers! How are even numbers inherently different from odd numbers?
Odd numbers in numerology are solar, masculine, acidic, electric, dynamic. When grouping odd numbers, one number will remain without its pair (1 and 3; 5 and 7; 9). These numbers are addends (they are added to something).
Even numbers are lunar, feminine, alkaline, magnetic, static. Numbers in this group are subtracted or reduced. They are static and remain motionless because they have even groups of pairs (2 and 4; 6 and 8).
Even numbers in numerology
It is well known that even numbers are those numbers that are divisible by two. What do even numbers mean regarding spiritual numerology? 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.
The number 2 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 in numerology
Numbers that are not divisible by two are called odd. 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 for a dead person even... 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 3 – 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 odd numbers. In interpreting odd numbers, one must understand: what seems to a person is not always what really exists. 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, the maturity of the mind is characterized by the ability to perceive paradoxes. Therefore, it takes a little more brainpower to explain odd numbers than to explain even numbers.
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...
Parity
If a number is written in decimal form last digit is an even number (0, 2, 4, 6 or 8), then the whole number is also even, otherwise it is odd.
42
, 104
, 11110
, 9115817342
- even numbers.
31
, 703
, 78527
, 2356895125
- odd numbers.
Arithmetic
- Addition and subtraction:
- H yotnoe ± H yotnoe = H good
- H yotnoe ± N even = N even
- N even ± H yotnoe = N even
- N even ± N even = H good
- Multiplication:
- H× H yotnoe = H good
- H× N even = H good
- N even × N even = N even
- Division:
- H yotnoe / H even - it is impossible to clearly judge the parity of the result (if the result is an integer, then it can be either even or odd)
- H yotnoe / N even = if the result is an integer, then it is H good
- N even / H even - the result cannot be an integer, and therefore have parity attributes
- N even / N even = if the result is an integer, then it is N even
History and culture
The concept of parity of numbers has been known since ancient times and was often given mystical meaning. So, in ancient Chinese mythology, odd numbers corresponded to Yin, and even numbers corresponded 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, it is customary to bring an even number of flowers only to funerals of the dead; in cases where there are many flowers in the bouquet, the evenness or oddness of their number no longer plays such a role.
Notes
Wikimedia Foundation. 2010.
- Odd parity
- Odd and even functions
See what “Odd numbers” are in other dictionaries:
Even and odd numbers- Parity in number theory is a characteristic of an integer that determines its ability to be divided by two. If an integer is divisible by two without a remainder, it is called even (examples: 2, 28, −8, 40), if not, odd (examples: 1, 3, 75, −19).... ... Wikipedia
Numbers- In many cultures, especially Babylonian, Hindu and Pythagorean, number is a fundamental principle underlying the world of things. It is the beginning of all things and the harmony of the universe behind them. external communications. Number is the basic principle... ... Dictionary of symbols
NUMBERS- ♠ The meaning of the dream depends on where exactly and in what form you saw the number you dreamed about, as well as on its meaning. If the number was on the calendar, this is a warning about what awaits you on that day important event, which will turn your whole... ... Big family dream book
ROOT OF A NUMBER- (root of number) The number x whose value to the power of r is equal to y. If y=xr, then x is the root of the r power of y. For example, in the equation y=x2, x is square root from y, and is written as follows: x=√ y=y1/2; if z=x3, then x is cubic... ... Economic dictionary
Pythagoras and the Pythagoreans- Pythagoras was born on Samos. The heyday of his life was in the 530s BC, and his death at the beginning of the 5th century. BC Diogenes Laertius, one of the famous biographers of ancient philosophers, tells us: Young and greedy for knowledge, he left his fatherland,... ... Western philosophy from origins to the present day
litters- (from the Greek soros heap) a chain of abbreviated syllogisms in which either the major or minor premise is omitted. There are two types of S.: 1) S., in which, starting from the second syllogism in the chain of syllogisms, a smaller premise is omitted; 2) S., in which... ... Dictionary of Logic Terms
"Sacred" meaning of numbers in beliefs and teachings- To the material “07.07.07. Lovers around the world believed in the magic of numbers” Since ancient times, numbers have played an important and multifaceted role in human life. Ancient people attributed special, supernatural properties to them; some numbers promised... ... Encyclopedia of Newsmakers
NUMEROLOGY- And; and. [lat. numero I consider and Greek. logos doctrine] A doctrine based on the belief in supernatural influence on the fate of a person, country, etc. combinations of certain numbers, numbers. ◁ Numerological, oh, oh. No predictions. * * * NUMEROLOGY… … Encyclopedic Dictionary
Random prime number- In cryptography, a random prime number is a prime number containing a specified number of bits in binary notation, the generation algorithm of which is subject to certain restrictions. Obtaining random prime numbers is... ... Wikipedia
lucky number- In number theory, a lucky number is a natural number of a set generated by a “sieve”, similar to the sieve of Eratosthenes, which generates prime numbers. Let's start with a list of integers, starting with 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,... ... Wikipedia
Books
- I'm doing math. For children 6-7 years old, Sorokina Tatyana Vladimirovna. The main objectives of the manual are to familiarize the child with the mathematical concepts of “addend”, “sum”, “minuend”, “subtrahend”, “difference”, “single/double digit numbers”, “even/odd…
· Even numbers are those that are divisible by 2 without a remainder (for example, 2, 4, 6, etc.). Each such number can be written as 2K by choosing a suitable integer K (for example, 4 = 2 x 2, 6 = 2 x 3, etc.).
· Odd numbers are those that when divided by 2 leave a remainder of 1 (for example, 1, 3, 5, etc.). Each such number can be written as 2K + 1 by choosing a suitable integer K (for example, 3 = 2 x 1 + 1, 5 = 2 x 2 + 1, etc.).
- Addition and subtraction:
- Hyotnoe ± H yotnoe = H good
- Hyotnoe ± N even = N even
- Neven ± H yotnoe = N even
- Neven ± N even = H good
- Multiplication:
- H× H yotnoe = H good
- H× N even = H good
- Neven × N even = N even
- Division:
- Hyotnoe / H otnoe - it is impossible to clearly judge the parity of the result (if the result integer, then it can be either even or odd)
- Hyotnoe / N even --- if the result integer, then it H good
- Neven / H even - the result cannot be an integer, and therefore have parity attributes
- Neven / N even ---if result integer, then it N even
The sum of any number of even numbers is even.
The sum of an odd number of odd numbers is odd.
The sum of an even number of odd numbers is even.
The difference of two numbers is the same evenness is theirs sum.
(eg 2+3=5 and 2-3=-1 are both odd)
Algebraic
(with + or - signs) sum of integers
has the same evenness is theirs sum.
(eg 2-7+(-4)-(-3)=-6 and 2+7+(-4)+(-3)=2 are both even)
The idea of parity has a lot different applications. The simplest of them are:
1. If in some closed chain objects of two types alternate, then there is an even number of them (and an equal number of each type).
2. If in a certain chain objects of two types alternate, and the beginning and end of the chain different types, then there is an even number of objects in it; if the beginning and end are of the same type, then the number is odd. (an even number of objects corresponds to odd number of transitions between them and vice versa !!! )
2". If an object alternates two possible states, and the initial and final states different, then the periods of an object’s stay in one state or another - even number, if the initial and final states coincide, then odd. (rewording clause 2)
3. Conversely: by the evenness of the length of an alternating chain, you can find out whether its beginning and end are of the same or different types.
3". Conversely: by the number of periods an object remains in one of two possible alternating states, you can find out whether the initial state coincides with the final state. (reformulation of point 3)
4. If objects can be divided into pairs, then their number is even.
5. If for some reason an odd number of objects were divided into pairs, then one of them will be a pair to itself, and there may be more than one such object (but there is always an odd number).
(!) All these considerations can be inserted into the text of the solution to the problem at the Olympiad, as obvious statements.
Examples:
Task 1. There are 9 gears on the plane, connected in a chain (the first with the second, the second with the third... the 9th with the first). Can they rotate at the same time?
Solution: No, they can't. If they could rotate, then two types of gears would alternate in a closed chain: rotating clockwise and counterclockwise (it has no meaning for solving the problem, in which one exactly direction the first gear rotates ! ) Then there should be an even number of gears, but there are 9 of them?! h.i.t.c. (the "?!" sign indicates a contradiction)
Task 2.
Numbers from 1 to 10 are written in a row. Is it possible to place + and - signs between them to get an expression equal to zero?
Solution: No, you can't. Parity of the resulting expression Always will match the parity amounts 1+2+...+10=55, i.e. sum will always be odd
. Is 0 an even number?! etc.
Before talking about even and odd numbers, it is worth understanding a few points about what groups of numbers there are. This is necessary so as not to try to figure out the evenness of the fraction.
What numbers do studies begin with in basic school?
Natural ones come first. They also first appeared historically. Humanity needed to count things. Moreover, when counting, zero is not used, so it is not included in the group of natural numbers. Here everything is an integer that is greater than one.
It is for them that the definition of parity is first given. To understand which number is odd, you need to remember the sign of even. It ends with one of the numbers: 0, 2, 4, 6, 8. All others will be odd. The minimum of them is equal to one. There is no maximum.
What numbers come next?
Whole. Their set already includes zero and all negative numbers. The chain of natural numbers was limited on the left, and continued indefinitely to the right. With integers there is an infinite number of numbers to the left of zero.
At this point, the definition of parity changes slightly. It should now be divisible by two without a remainder. This means that odd numbers when divided by two give an answer with a remainder.
Moreover, a general notation is even introduced: for even numbers - 2n, odd ones - (2n+1). If for naturals there is only no maximum even or odd, then for integers there is no minimum.
What then?
Rational (another name is real) numbers. In addition to those already mentioned, this set also includes fractions. That is, numbers that can be represented as two. The first of these is the numerator and is represented as an integer. The second is the denominator, which is never zero.
By the way, the concept of parity is not introduced for them. Therefore, odd numbers written as a fraction do not exist at all.
What results do operations with even and odd numbers produce?
They can be considered in order of complexity of the arithmetic operation. Then addition and subtraction will come first and second. It doesn't matter which one is executed, the answer will depend only on the initial pair of numbers. For example, if the original numbers are even, then the result of the action will be divided by two. The same result will be if it is the difference or the sum of odd numbers. To get an odd number, you have to add or subtract an even number from an odd number.
This can be easily verified using their common record. For example, adding two even numbers: 2n+2n = 4n = 2*2n. Here 2n is an even number, which is also multiplied by two. This means that it will definitely be divisible by two. That is, the answer is even.
When adding even and odd, we have the following notation: 2n + (2n + 1) = 4n + 1. The first term is an even number, to which one is added. The last term will not allow you to divide this result by two completely.
The third action is multiplication. When executed, there will always be an even answer if there is at least one even factor. In a situation where two odd numbers are multiplied, the result will be odd.
To illustrate the latter, you will need to write this: (2n + 1) * (2n + 1) = 4n + 2n + 2n + 1 = 8n + 1. Again, the first term is an even number, and one will make it odd.
With the fourth action - division - everything is not so simple. You can start with two even ones. Firstly, it may turn out to be a fraction, then there is no question of parity. Secondly, the result is an integer. But even then it is impossible to obtain an unambiguous answer to the question about future parity. It can only be evaluated after division has been completed. The answer can be either even or odd.
If an odd number is divided by an even number, the answer is always fractional. This means that its parity is not determined.
When division involves odd numbers, the result may also be a fraction. But if the answer is integer, then it will definitely be odd.
When dividing even by odd, as in the previous situation, two options are possible: a fraction or an integer. In the second case it will always be even.