The Wikipedia page on polar cones contains the following statement: "For a closed convex cone C in X, the polar cone is equivalent to the polar set for C".
I'm not sure why this is true, using the notation I have learned, for a convex cone $C \in \mathbb{K}^n$, the polar cone is:
$$ C^\Delta = \{y \in \mathbb{K}^n | \forall x \in C: y^T x \le 0\} $$
Whereas the polar set would be:
$$ C^\circ = \{y \in \mathbb{K}^n | \forall x \in C: y^T x \le 1\} $$
How can these be the same?