H is a hyperplane in a linear space X if and only if there exists a nonzero linear functional f X ' such that H x X f(x) c for some c We use Hf (c) to denote the specific hyperplane corresponding to the c level contour of the linear functional f

Question: H is a hyperplane in a linear space X if and only if there exists a nonzero linear functional f X' such that H

H is a hyperplane in a linear space X if and only if there exists a nonzero linear functional f ∊ X' such that
H = {x ∊ X : f(x) = c}
for some c ∊ ℜ.
We use Hf (c) to denote the specific hyperplane corresponding to the c-level contour of the linear functional f.

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