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:
“All’s oblique;
There’s nothing level in our cursed natures
But direct villainy. Therefore be abhorred
All feasts, societies, and throngs of men!”
—William Shakespeare (1564–1616)
“The cunningest dissimulation is when a man pretends to be caught in the traps others set for him; and a man is never so easily over-reached as when he is contriving to over-reach others.”
—François, Duc De La Rochefoucauld (1613–1680)