# Mathematical properties of establishment in integers

Perhaps the best thing, before moving forward on a definition of each of the mathematical properties that can be found in the Establishment of integers, is to briefly review some concepts, which will allow you to understand these laws in your mathematical context Precise.

## Fundamental definitions

In this way, it may also be useful to focus this theoretical review on two specific notions: Integers and Integer Radiation, because they are directly related to the nature of the numerical elements and the operation mathematics on the basis of which each of these properties arises. Here’s each one:

## The Whole Numbers

In this sense, it will begin by saying then that mathematics has defined integers as those numerical elements with which you can account or represent whole or exact amounts, that is, that in them don´t take place neither the amounts fractional, or those with decimal expressions.

Similarly, this discipline has pointed out that integers can also be identified as the elements that make up the eponymous numeric set, which is also known as the Z numerical set, a collection where the integers grouped as follows:

Positive integers: First, positive integers can be found as a subset of Z, a grouping that will also be known as set N, or set of Natural Numbers. These elements will be characterized by being located in the number line to the right of zero, from where they will extend from 1 to the . They can count the elements of a grouping, or express an accounting quantity.

Negative integers: on the other hand, within the Z set you will also find the negative integers, which will be understood as the inverses of the positive numbers, which is why they will be found in the number line to the left of the zero, from where it is range from -1 to -O. Thanks to negative integers, the Z set can be used when accounting for debt or lack of a specific amount.

Zero: Finally, zero will also be part of the natural numbers set. However, this element will not be considered a number as such, but as the total absence of quantity. Therefore, it isn´t assumed as negative and positive, while being conceived as inverse of itself.

## Integer establishment

In another order of ideas, it will also be necessary to make a brief revision to the definition of Radication in whole numbers, which has been explained by Mathematics as an operation in which two integers try to determine a third, which complies with the ownership that being elevated to one of them, results in the other, hence the Establishment of integers is also seen by some authors as an inverse form of Empowering.

Thus, this discipline states that the Establishment of integers will be established between three numerical elements, each defined in turn as follows:

Index: this will be one of the numbers on which the Radication operation will be established. Your mission will be to point out to the root how many times you must multiply yourself, in order to result in the Radicando.

Radicando: for its part, this element will be the second on which the Radication operation will be established. It will serve to point out to the root what the correct result should be, as long as it is raised to the index.

Root: Finally, the Root will be interpreted as the final result of the operation, that is, as the number that will have the quality that once raised to the Index, results in the Radicando.

## Properties of the Establishment of Integers

With these definitions in mind, it may then be much easier to address an explanation of each of the two mathematical laws that can be found in reference to the Establishment of whole numbers, and which have been explained in turn from the next Way:

## The two signs of square roots

In this sense, the first mathematical property that will be found in the Establishment of integers will be that always and without exception the square roots of integers will have two signs, since whether it is negative, or positive, when raised to the square will result in a positive establishment. An example of this property may be the following:

√25 = 5  →  52 = 25
√25 = -5 → -5 = -5 . -5= 25

## The positive character of the square root establishment

Likewise, the Mathematics notes that in the operation of Radication of whole numbers the property indicating that always and in any case the establishment of square roots must be a positive integer, as well as non-zero, since it is considers it impossible, mathematically speaking a file operation in which the establishment is negative, that is, that there is no or no viable solution, since there is no number that raised squared can result in a negative whole number .