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Accumulation point of the sequence

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1) Suppose || · || and || · ||' are two arbitrary norms on Rd. Prove that || · ||'', defined by ||x||'' = ||x|| + ||x||', x ∈ Rd,is also a norm on Rd.

2) Suppose {xn}∞n=1 is a sequence in Rd converging to y. Show that y is the only accumulation point of the sequence.

Reference no: EM131396980

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