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Math Help - is this sequence convergent in this vector space

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    is this sequence convergent in this vector space

     (1,0,0,....), (0,1,0,0,....) , ...........

    V is the vector space of all sequences of real numbers converge to zero.
    and norm: |(x_{1},x_{2},....)|=\max_{i\geq1}{|x_{i}|}
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  2. #2
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    Quote Originally Posted by silversand View Post
     (1,0,0,....), (0,1,0,0,....) , ...........

    V is the vector space of all sequences of real numbers converge to zero.
    and norm: |(x_{1},x_{2},....)|=\max_{i\geq1}{|x_{i}|}
    No, that sequence does not converge because it is not Cauchy. The distance between any two elements of the sequence (as measured by the norm of their difference) is 1.
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