Absolute Value - Absolute Value Function

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:

    ... woman was made first for her own happiness, with the absolute right to herself ... we deny that dogma of the centuries, incorporated in the codes of all nations—that woman was made for man ...
    —National Woman Suffrage Association. As quoted in The History of Woman Suffrage, vol. 3, ch. 27, by Elizabeth Cady Stanton, Susan B. Anthony, and Matilda Joslyn Gage (1886)

    As a medium of exchange,... worrying regulates intimacy, and it is often an appropriate response to ordinary demands that begin to feel excessive. But from a modernized Freudian view, worrying—as a reflex response to demand—never puts the self or the objects of its interest into question, and that is precisely its function in psychic life. It domesticates self-doubt.
    Adam Phillips, British child psychoanalyst. “Worrying and Its Discontents,” in On Kissing, Tickling, and Being Bored, p. 58, Harvard University Press (1993)