Nichtnegativfunktion

A Nichtnegativfunktion, or non-negative function in English, is a mathematical function whose output values are always greater than or equal to zero. For any input value in the function's domain, the corresponding output must be non-negative. This property is fundamental in various areas of mathematics and its applications.

For example, the absolute value function, denoted as |x|, is a classic non-negative function because the result of taking the absolute value of any real number is always zero or a positive number. Another example is the square root function, √x, when considering its principal (non-negative) root, as its output is always non-negative for a non-negative input.

In probability theory, probability density functions and probability mass functions are inherently non-negative functions, as the probability of any event cannot be negative. Similarly, in optimization problems, objective functions that represent quantities like cost or distance are often required to be non-negative, reflecting the physical impossibility of negative costs or distances. The concept ensures that the function's values are physically or conceptually meaningful in contexts where a negative outcome is not permissible.