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Showing that a continuous function achieves a maximum implies compact

  1. Aug 21, 2013 #1
    upperbound_zpsb0dca753.png

    I've prove everything except for the fact that E is bounded below. It would appear that you would need to know something about the functions taking a minimum value as well to show this using my method, so perhaps there is another way of thinking about things to show a lower bound?
     
  2. jcsd
  3. Aug 21, 2013 #2

    Dick

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    f(x)=(-x) is also continuous.
     
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