In mathematics, a set of a real-value function f in n variables is a set of the form { (x1,...,xn) | f(x1,...,xn) = c }
where c is a constant. That is, it is the set where the function assumes a given constant value.
When the number of variables is equal to two, this is a level curve (contour line), if the number of variables is equal to three then this is a level area. For higher values of n, we speak for the level range of a level surface.
More specifically, a level curve is the set of all real-life roots of a comparison in two variables x1 and x2. A level surface is the set of all real-life roots of a comparison in three variables x1, x2 and x3. A level surface is the set of all real-world worels of an equation in n (n> 3) variables.
A comparison of the form { (x1,...,xn) | f(x1,...,xn) ≤ c }
is called a sub-level set of f. Also see
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