3.2.13 Examples with Monotonic Functions

Consider the exponential function , which is a monotonically increasing function. An example evaluation follows:

with

Similar functions include for all , for all , and for all , .

The floor function is both monotonically increasing and piecewise constant. Consider the evaluation of , , as a piecewise constant function:

with

and as a monotonically increasing function:

with

The floor function should therefore be handled as a monotonically increasing function, for large arguments.

Consider the negation function , which is a monotonically decreasing function. An example evaluation follows:

with

The function is similar, for , .

Jeff Tupper

March 1996