# What is absolute value?

## What Does absolute value Mean

The notion of absolute value is used in the field of mathematics to name the value that has a number beyond its sign. This means that the absolute value, which is also known as the modulus , is the numerical magnitude of the figure regardless of whether its sign is positive or negative.

Take the case of the absolute value 5 . This is the absolute value of both +5 (5 positive) and -5 (5 negative). The absolute value, in short, is the same in the positive number and in the negative number: in this case, 5 . It should be noted that the absolute value is written between two parallel vertical bars; therefore, the correct notation is | 5 | .

The definition of the concept indicates that the absolute value is always equal to or greater than 0 and is never negative . From what has been said before, we can add that the absolute value of the opposite numbers is the same; 8 and -8 thus share the same absolute value: | 8 | .
The absolute value can also be understood as the distance between the number and 0 . The number 563 and the number -563 are, on a number line, the same distance from 0 . That, therefore, is the absolute value of both: | 563 | .
The distance between two real numbers , on the other hand, is the absolute value of their difference. Between 8 and 5 , for example, there is a distance of 3 . This difference has an absolute value of | 3 | .
The concept of absolute value is present in several subjects of mathematics, and the vector is one of them; more precisely, it is in the vector norm where we are faced with a similar definition. Before continuing, however, it is necessary to define Euclidean space , since these concepts are conjugated in this area.
We understand by Euclidean space a kind of geometric space in which Euclid's axioms are satisfied . An axiom is a proposition whose clarity is such that it does not require a proof to be admitted; specifically in the field of mathematics, this is the name given to the fundamental and unprovable principles on which theories are built .
Euclides , for his part, was born in Greece around 325 BC. C., and his dedication to numbers made him worthy of the title "Father of Geometry." His most important work is a collection of thirteen books grouped under the heading " Elements ", where the aforementioned axioms (also known as presented the postulates of Euclid ), and we'll see briefly below:

1) if we take any two points, it is possible to join them by means of a line;
2) it is possible to extend continuously all the segments, regardless of the direction;
3) the circumferences can originate from any point, which will be taken as its center, and its radius can acquire any value;
4) any pair of right angles is congruent;
5) it is possible to draw a single line parallel to another from a point outside the latter.
Having exposed the bases of the Euclidean spaces, we can say that the vectors can be represented in them in the form of segments that are oriented between any two points. If we take a vector, we can define its norm as the distance between two points, which serve as a limit; so much so, that in a Euclidean space this norm corresponds to the module, that is, to the length of said vector.
Like the absolute value, the modulus of a vector is always a positive number or zero , since it represents a length, a distance. In this case, as in many others, associating this magnitude with a sign could cause unnecessary complications.
In the field of video game programming, on the other hand, the absolute value can appear on numerous occasions, depending on the methodology of each developer. For example, when calculating the current speed of a character, we can ignore the direction in which it is traveling and simply contemplate the segment that exists between 0 and maximum speed, applying acceleration accordingly; finally, it is enough to multiply the resulting value by the direction vector of the character to transfer it.

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