Limit of $x_n$ is unique in a pre-Hilbert space

Question

If the limit of $x_n$ exists, then it is unique in pre-Hilbert space. How can I prove that?

The same way you do it for Hilbert spaces. Presumably the exact same string, in fact. — , May 15 '20 at 10:34

score 1 · Answer 1 · answered May 15 '20 at 10:53

1

Suppose $x_n \to x,y.$ Then $$\|x-y\|=\|x-x_n+x_n-y\|\leq \|x_n-x\|+\|x_n-y\|\to 0.$$

answered May 15 '20 at 10:53

Sahiba Arora

1 Answers1