Recent content by werdna91

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    Prove that the interior of the set of all orthogonal vectors to a is empty.

    But by assuming that B(r, x) is in S, I thought I could conclude that a•u=0? Do you think there is a better approach for me to prove this?
  2. W

    Prove that the interior of the set of all orthogonal vectors to a is empty.

    Quinzio, I believe that is true. If S^int is empty, then S = the boundary of S. Here is the proof I came up with, can somebody verify it?Given S, we know that S^c = { y in R^n : a•y ≠ 0 } which is not empty. Let x be in S and suppose that its interior is not empty. Then there exists an r > 0...
  3. W

    Prove that the interior of the set of all orthogonal vectors to a is empty.

    Homework Statement Here is a picture of the problem: http://img84.imageshack.us/img84/1845/screenshot20100927at111.png If the link does not work, the problem basically asks: Let "a" be a non-zero vector in R^n. Let S be the set of all orthogonal vectors to "a" in R^n. I.e., a•x = 0 (where •...