## prove that the euclidean space is complete

(This proves the theorem which states that the medians of a triangle are concurrent.) (f,f) ≥ 0 and (f,f) = 0 iﬀ f = 0. 15-11 Completing the Euclidean Plane. In every such space, we define absolute values of vectors by \[|x|=\sqrt{x \cdot x}.\] (This root exists in \(E^{1}\) by formula (ii).) Continuous preferences in Euclidean space Assume that the choice set X is a subset of Euclidean n-space

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