In mathematics, a level set of a real-valued function f of n variables is a set of the form
that is, a set where the function takes on a given constant value c.
When the number of variables is two, a level set is generically a curve, called a level curve, contour line, or isoline. When n = 3, a level set is called a level surface (see also isosurface), and for higher values of n the level set is a level hypersurface.
A set of the form
is called a sublevel set of f (or, alternatively, a lower level set or trench of f).
is called a superlevel set of f.
A level set is a special case of a fiber.
Read more about Level Set: Properties
Famous quotes containing the words level and/or set:
“It is only for a little while, only occasionally, methinks, that we want a garden. Surely a good man need not be at the labor to level a hill for the sake of a prospect, or raise fruits and flowers, and construct floating islands, for the sake of a paradise. He enjoys better prospects than lie behind any hill. Where an angel travels it will be paradise all the way, but where Satan travels it will be burning marl and cinders.”
—Henry David Thoreau (1817–1862)
“Women are to be lifted up to a physical equality with man by placing upon their shoulders equal burdens of labor, equal responsibilities of state-craft; they are to be brought down from their altruistic heights by being released from all obligations of purity, loyalty, self-sacrifice, and made free of the world of passion and self-indulgence, after the model set them by men of low and materialistic ideals.”
—Caroline Fairfield Corbin (b. c. 1835–?)