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Let $ ( , ):V \times V \rightarrow \mathbb{R} $ be a real-valued non-degenerate inner product on the real vector space $V$.

Given, for all $v \in V$ we have $(v,v) \geq 0$

Now prove that if $(x,x)=0$ then $x=0$ for $x \in V$, that is, prove that the inner product is Euclidean.

I think it is easy, but I cannot find it. Thank you.