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Math Help - Proof for banach Space 1

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    Proof for banach Space 1

    Prove that Xn converges to X then normed Xn converges to normed X

    Anyone can help?
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by neset44 View Post
    Prove that Xn converges to X then normed Xn converges to normed X

    Anyone can help?
    This is horrible notation. I assume your saying that \left\{x_n\right\} is a sequence in a Banach space B and x_n\to x and to prove that it follows that \|x_n\|\to\|x\|, right?

    Hint:

    Spoiler:


    |\|x_n\|-\|x\||\leqslant\|x_n-x\|

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