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Thread: Interesting problem

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    Supreme Member seanieg89's Avatar
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    Interesting problem

    Here is an interesting problem. If you are not comfortable with higher dimensional spaces, replace "affine hyperplane" with "line" (not necessarily through the origin), and fix n=2 in the below.

    Suppose we have finitely many affine hyperplanes
    and suppose a point is chosen arbitrarily.

    Prove that any sequence defined by:

    is bounded, where denotes orthogonal projection onto and the sequence in is chosen arbitrarily.

    Is your bound independent of your choice of sequence ?
    Last edited by seanieg89; 20 Sep 2017 at 3:38 PM.

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