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:
“I love thee to the level of everyday’s
Most quiet need, by sun and candle-light.
I love thee freely, as men strive for Right;
I love thee purely, as they turn from Praise.
I love thee with the passion put to use
In my old griefs, and with my childhood’s faith.”
—Elizabeth Barrett Browning (1806–1861)
“To find the length of an object, we have to perform certain
physical operations. The concept of length is therefore fixed when the operations by which length is measured are fixed: that is, the concept of length involves as much as and nothing more than the set of operations by which length is determined.”
—Percy W. Bridgman (1882–1961)