Borsuk-Ulam theorem

Statement
Let $$S^m$$ denote the $$m$$-dimensional sphere (embedded in $$\R^{m+1}$$) and $$\R^m$$ denote $$m$$-dimensional Euclidean space. Then, given any continuous map $$f:S^m \to \R^m$$, there is a point $$x \in S^m$$ such that $$f(x) = f(-x)$$.