Absolute Value Function
The real absolute value function is continuous everywhere. It is differentiable everywhere except for x = 0. It is monotonically decreasing on the interval (−∞,0] and monotonically increasing on the interval [0,+∞). Since a real number and its negative have the same absolute value, it is an even function, and is hence not invertible.
Both the real and complex functions are idempotent.
It is a piecewise linear, convex function.
Read more about this topic: Absolute Value
Famous quotes containing the words absolute value, absolute and/or function:
“One may almost doubt if the wisest man has learned anything of absolute value by living.”
—Henry David Thoreau (1817–1862)
“The revolutionary spirit is mighty convenient in this, that it frees one from all scruples as regards ideas. Its hard absolute optimism is repulsive to my mind by the menace of fanaticism and intolerance it contains. No doubt one should smile at these things; but, imperfect Esthete, I am no better Philosopher. All claim to special righteousness awakens in me that scorn and anger from which a philosophical mind should be free.”
—Joseph Conrad (1857–1924)
“The art of living is to function in society without doing violence to one’s own needs or to the needs of others. The art of mothering is to teach the art of living to children.”
—Elaine Heffner (20th century)