Cantor's function

Cantor's function, also known as the Cantor staircase, is a mathematical construct that illustrates a continuous function that is not monotonic and has a peculiar property: it increases from 0 to 1, yet is flat over most of its interval. It is created using the Cantor set, which involves removing the middle thirds of a line segment repeatedly. The function remains constant on these removed segments and increases only on the remaining points. This illustrates concepts of continuity and measure in mathematics, specifically showing that some continuous functions can have a complicated structure despite their simple appearance.