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:
“[A writer] should try not to be too far, personally, below the level of his work.”
—Elizabeth Bowen (1899–1973)
“He could walk, or rather turn about in his little garden, and feel more solid happiness from the flourishing of a cabbage or the growing of a turnip than was ever received from the most ostentatious show the vanity of man could possibly invent. He could delight himself with thinking, “Here will I set such a root, because my Camilla likes it; here, such another, because it is my little David’s favorite.””
—Sarah Fielding (1710–1768)