TITLE: Uses of step functions
QUESTION [5 upvotes]: My highschool teacher has informally told us about what continuity is and used step functions as an example of a discontinuous function.
The Wikipedia page for it links to a lot of other kind of step functions, such as the Heaviside step function.
What are some uses of these step functions to mathematicians at higher levels (or even in highschool)?

REPLY [5 votes]: Two of the most frequently used step functions are the "floor" and "ceiling" functions.
The floor function takes a real number and returns the largest integer(whole) number less then or equal the real number.  For a positive real number this is equivalent to cutting off all the numbers after the decimal place.
The ceiling function returns the smallest integer number greater then the number given.
They are useful in rounding off and often arise in cases where there is some sort of calculation that results in a real number but only the whole part is meaningful.