absolutväärtust

Absolutväärtust, also known as the magnitude or modulus of a number, represents the distance of that number from zero on the number line. It is a fundamental concept in mathematics. For any real number x, its absolute value is denoted by |x|.

The definition of absolute value is piecewise. If a number is non-negative (greater than or equal to zero), its absolute value is the number itself. For example, |5| = 5 and |0| = 0. If a number is negative (less than zero), its absolute value is its additive inverse, meaning the number multiplied by -1. For instance, |-3| = -(-3) = 3.

This concept has several key properties. The absolute value of any number is always non-negative. That is, |x| ≥ 0 for all real numbers x. Also, |x| = |-x|, meaning a number and its opposite have the same absolute value. The triangle inequality is another important property, stating that for any two real numbers x and y, |x + y| ≤ |x| + |y|.

Absolute value is used extensively in various areas of mathematics, including algebra, calculus, and geometry. It is crucial for defining distances between points, solving equations involving inequalities, and understanding concepts like norms in vector spaces. In programming, absolute value functions are commonly available for numerical operations.