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 and/or function:
“We have imagined ourselves a special creation, set apart from other humans. In the last twentieth century, we see that our poverty is as absolute as that of the poorest nations. We have attempted to deny the human condition in our quest for power after power. It would be well for us to rejoin the human race, to accept our essential poverty as a gift, and to share our material wealth with those in need.”
—Robert Neelly Bellah (20th century)
“We are thus able to distinguish thinking as the function which is to a large extent linguistic.”
—Benjamin Lee Whorf (1897–1934)