," where
is a real number. This function remains constant from one integer to the next, and then gives a sudden jump. The actual fact is that, though continuous functions are more familiar, they are the exceptions: there are infinitely more discontinuous functions than continuous ones.
Many functions are discontinuous for one or several values of the variable, but continuous for all other values. Take as an example
. The function
passes through all values from -1 to 1 every time that
