Monotonic

Mathematical term:

A function is called strictly monotonic if f(x) always increases as x increases.

We can express this in differential calculus by saying:

f'(x)>0 for all x.

Examples include (letting y = f(x)):

y=x
y=log(x)
y=-1/x (if x != 0)
y=x^3

Strictly speaking, a monotonic function can be either monotonically increasing or decreasing unless otherwise specified. A function is monotonically increasing if x > y implies f(x) >= f(y). A function is strictly monotonically increasing if x > y implies f(x) > f(y) (note the lack of an equals sign).

Related ideas are bitonic function and constant function.

Mon`o*ton"ic (?), Mon`o*ton"ic*al (?), a.

Of, pertaining to, or uttered in, a monotone; monotonous.

"Monotonical declamation."

Chesterfield.

 

© Webster 1913.