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:
“No man loses ever on a lower level by magnanimity on a higher.”
—Henry David Thoreau (1817–1862)
“I set out on this ground, which I suppose to be self evident, “that the earth belongs in usufruct to the living”: that the dead have neither powers nor rights over it.”
—Thomas Jefferson (1743–1826)