Sístækkandi

Sístækkandi is an Icelandic term that translates to "steadily increasing" or "continuously growing." It is a mathematical concept used to describe a function whose value either increases or stays the same as the independent variable increases. More formally, a function f(x) is sístækkandi if for any two values x1 and x2 in its domain, where x1 ≤ x2, it follows that f(x1) ≤ f(x2). This means that the function never decreases.

In contrast to strictly increasing functions, which must increase whenever the independent variable increases (f(x1) < f(x2) for x1 < x2), sístækkandi functions allow for periods where the function's value remains constant. This distinction is important in calculus and analysis. For example, a step function that stays at a certain value for an interval before jumping to a higher value would be considered sístækkandi but not strictly increasing.

The concept of sístækkandi is fundamental in various fields, including economics, where it can describe economic indicators that generally rise over time, or in probability, where cumulative distribution functions are always sístækkandi. Understanding whether a function is sístækkandi or strictly increasing can provide crucial insights into the behavior of systems and models.