Odd and even numbers help us to identify which of them can be divisible by two or by another number divisible by groups of two. But to learn more about these values, we invite you to continue with us in this article.

even-and-odd-numbers

Odd and even numbers

When talking about odd numbers, the way to solve the division of a number divisible by two is indicated, which is also a whole number. On the other hand, it is said that it is divisible by groups of two; In mathematics, various problems can be solved when the number is divisible by numbers from a 2.

The operations are performed by subtracting or adding 2 digits to the number so that a decimal fraction is not produced. For example, the number 10 is an even number since dividing it by 2 results in a number that multiplied by 2, its result is the initial number 10.

A number is said to be odd when they are not even, so they are not multiples of 2. When 2 values ​​are added, the result is still an odd number; It is also said that the odd number is the one that being even, a number 1 is added and the value as such is obtained, let's see this example M = 2 xn + 1, where M is the odd number and "n" is any number.

There is also a hypothesis which says that every integer that is not even, but is a multiple of 2, is considered an odd number; so, you can add or subtract 2 to that odd number, obtaining then another even number. A mathematical axiom says the following:

"An integer is odd if and only if there is another integer"

Formulas for even numbers

There are primary formulas to generate even numbers, they are formed by creating multiples of 2 with some natural numbers chosen at random. These can be as follows: 0 + 2 = 2, 2 + 2 = 4, 2 + 2 + 2 = 6, 2 + 2 + 2 + 2 = 8 and so on until reaching values ​​that can reach the infinite.

These values ​​result with the same value, when the multiplication is applied let's see: 2 × 1 = 2, 2 × 2 = 4, 2 × 3 = 6, 2 × 4 = 8. In the same way, they can be extended to the largest number that we want; The consecutive series of even numbers is created from the number 2, from then on 2 are added or added to the next number and consecutively, all the even numbers are obtained.

The formula to generate these numbers without the need to lengthen a list is the following P = 2n, where (n) is any natural number. Consequently, a series of even integers can be generated from minus infinity to plus infinity.

Formulas for odd numbers

We already know that the odd number is an even number to which 1 is added. In this way we would have the problem solved; but from the mathematical point of view, the formula for its creation would be as follows: I = 2n + 1, already seen previously, where (n) is any natural number.

In this way the formula is generated in series, starting from 0; 2 (0) + 1 = 1, then 2 (1) + 1 = 3, 2 (2) + 1 = 5, 2 (3) +1 = 7, as we see the value «n» we are assigning it in the formula a consecutive series of numbers starting from "0" and we obtain the group of odd numbers, adding any number could reach infinity.

Properties and characteristics

Each of these numbers has properties that must be respected by certain laws of mathematics. We will begin by explaining the one related to even numbers, which are easier to use in operations, because being divisible by 2, the processes tend to be friendlier.

Of the even numbers

We can start by saying that one of the first properties is that it has an infinite condition either for the natural numbers or the integers (…… 2, -2, 4, -4, 8, -6,…).

In the same way, even numbers contain the same elements as natural numbers. The multiples of 2 pairs form an arithmetic sequence with the necessary condition of the number 2 and using 0 as the first term; Likewise, the ratio of the set of even natural numbers is also the set of odd natural numbers, although disjoint, it is united by its connection with the N (Natural) numbers.

Even numbers have a single even prime number, which is the number 2: the other even numbers are composite numbers since they admit two divisors. Likewise, the set of «N» in ordered pairs and with a relation less than 0 (<), where that number represents the minimum and the first even number.

Another important property of even numbers is that the addition or subtraction of two natural numbers with an even number power and an exponent other than 0 always results in an even number. On the other hand, the quotient of two even numbers (that are not divisors of 0, even or odd), always the result will also be an even number.

Also, the square of an even number "N" is considered a property, resulting in another even number. Consequently, the square root of an even number is also another even number.

Of the odd numbers

The properties of odd numbers have some interesting conditions and relationships. For example, the odd series is infinite, since it is the even series inscribed in the odd ones, so that all odd is equal to an even number plus 1. Another condition is the following, the first term for which is the number 1, is also the first number in the series of "N" numbers.

Half of all the numbers "N" and between god are odd the rest are even. Another property indicates that the infinite series of prime numbers (not including the number 2), includes the odd series, this implied that otherwise there would be prime numbers in the series of even number messes.

Finally, it is always good to be up to date with the knowledge and the way in which numbers are handled in mathematics. Parents should focus on tasks dedicated to odd and even numbers for kids when they are taking the first steps in primary education; However, the identification is very simple, just by knowing that a number ends in 2, it is determined that it is an even number.

Learn more about these numbers by reading the following article related to this topic What are decimal numbers?