Let $X$ be infinite dimensional normed linear space. Then prove that there exist a sequence $\{x_n\}$ in $X$ such that $\|x_n\|=1$ and $\|x_n-x_m\|>1$ for all $n,m=1,2,...,n!=m$.
Can this be solved by using the riesz lemma?
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1Yes, use the Riesz lemma and construct the sequence recursively. – Nate Eldredge Apr 03 '18 at 02:34
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Can you please provide some hints. Thank you – Ppp Apr 03 '18 at 02:35
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Is this for a Banach space? You did not say. – DanielWainfleet Apr 03 '18 at 08:58
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@DanielWainfleet It is for any normed linear space – Ppp Apr 19 '18 at 06:27