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Mar 29, 2014 at 9:31 comment added user40023 OK, it works, thanks. Moreover, taking $v_1, v_2, \ldots \in \mathbb{R}^d$ equidistributed over $\mathbb{S}^{d-1}$ it follows that $|S| \sim n / 2$ as $n \to \infty$.
Mar 29, 2014 at 4:52 history answered Christian Remling CC BY-SA 3.0