Absolutwerten

Absolutwerten, also known as absolute value, is a mathematical concept that represents the distance of a number from zero on the number line. It is always a non-negative quantity. The absolute value of a number x is denoted by |x|.

For any real number x, the absolute value is defined as:

If x is greater than or equal to 0, then |x| = x.

If x is less than 0, then |x| = -x.

For example, the absolute value of 5 is |5| = 5, because 5 is positive. The absolute value of -7 is |-7| = -(-7) = 7, because -7 is negative. The absolute value of 0 is |0| = 0.

This concept is fundamental in various areas of mathematics, including algebra, calculus, and geometry. It is used in defining distances between points, in solving equations and inequalities, and in understanding the behavior of functions. For instance, the distance between two numbers a and b on the number line is given by |a - b|.

In programming and computer science, absolute value functions are commonly available in standard libraries to perform calculations where only the magnitude of a number is relevant. The property that |x| is always non-negative makes it useful for ensuring that results remain positive, regardless of the sign of the input.