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Is the set bounded

  1. Oct 2, 2008 #1
    Is the set S = {(x,y): |x| + |y| <= 2} bounded? If so how do i prove it?

    looking at the graph i believe that S is bounded by 2 and -2, but i'm not sure if i'm correct and i don't know how to prove it.

  2. jcsd
  3. Oct 3, 2008 #2


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    I'm assuming when you say bounded, you mean with respect to "Euclidean distance."

    If so, here's a hint: |x|^2 + |y|^2 = (|x|+|y|)^2 - 2|x||y|.
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