Question: a) A subset E of Rn is said to be sequentially compact if and only if every sequence xk E has a convergent subsequence

a) A subset E of Rn is said to be sequentially compact if and only if every sequence xk ∈ E has a convergent subsequence whose limit belongs to E. Prove that every closed ball in Rn is sequentially compact.
b) Prove that Rn is not sequentially compact.

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