Högerkontinuerliga

Högerkontinuerliga is a term used in mathematics, specifically in the study of real analysis and calculus. It describes a property of a function at a particular point. A function f is said to be right-continuous at a point x if the limit of the function as it approaches x from the right is equal to the function's value at x. Mathematically, this is expressed as lim_{y->x+} f(y) = f(x).

This definition implies that as the input values to the function get arbitrarily close to x from values greater than x, the output values of the function get arbitrarily close to f(x). It is important to note that a function can be right-continuous at a point without being left-continuous. Left-continuity is defined similarly, but the limit is taken as y approaches x from the left: lim_{y->x-} f(y) = f(x).

If a function is both right-continuous and left-continuous at a point, then it is continuous at that point. Therefore, continuity at a point is a stronger condition than either right-continuity or left-continuity alone. The concept of right-continuity is particularly relevant when dealing with functions that may have jump discontinuities or are defined piecewise. For instance, the Heaviside step function, which is zero for negative inputs and one for non-negative inputs, is right-continuous at x=0 but not left-continuous there.