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:
“To Time it never seems that he is brave
To set himself against the peaks of snow
To lay them level with the running wave,
Nor is he overjoyed when they lie low,
But only grave, contemplative and grave.”
—Robert Frost (1874–1963)
“What is love itself,
Even though it be the lightest of light love,
But dreams that hurry from beyond the world
To make low laughter more than meat and drink,
Though it but set us sighing?”
—William Butler Yeats (1865–1939)