A step function is a piecewise-defined function in which every piece is a horizontal line segment or a point.
Let the function shown be defined for all the integers as
This function is made up of infinitely many discrete points each of which have a -coordinate of either or .
Consider the function, where .
This function is made up of infinitely many horizontal segments, each of which includes the right endpoint but not the left endpoint.
This step function is called the Heaviside Function. It may look very simple, but it is extremely important in electrical engineering and control theory.