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Math Help - left-invariant complete metric on S_\infty

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    left-invariant complete metric on S_\infty

    Let S_{\infty} be the group of all permutations of \mathbb{N}, viewed as a subspace of Baire space \mathcal{N}.
    How do I prove that there is no left-invariant complete metric on S_{\infty}?

    A metric is left-invariant if d(xy, xz)=d(y, z), for all x, y, z.

    Thank you.
    Last edited by harriette; January 16th 2010 at 12:37 PM.
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