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  3. 112 prove a b c andd proposition 1118 equivalence of...

Question: 112 prove a b c andd proposition 1118 equivalence of...

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1.12 Prove a, b, c, andd Proposition 1.1.18 (Equivalence of li, P. loo). Let Rn be a Euclidean space, and let rhbe a sequence of points in R. We write (k) ,n,弌) E R is the jth co- ,xn) be a point in Rn. Then the ), 1. e. , for j = 1,2 ordinate of alk) ER. Let following four statements are equivalent: (x1, (a) ((k) (b) (r()m converges to a with respect to the tari-cab metric d (c) (r()) converges to a with respect to the sup norm metric d (d) For every 1-j-n, the sequence (a(k)/k=rn converges to converges to a with respect to the Euclidean metric da. . Notice that this is a sequence of real numbers, not of points in Rn

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