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I was asked to prove this in my 3rd weak in college.

"Let $A$ be a nonempty set of real numbers, bounded above. Suppose exists $K>0$ so that for every two different numbers $x,y\in A: |x-y|>K$. Prove: $A$ has a maximum element."

Thank you in advance.

  • 2
    3rd weak? I didn’t realize that college was such a draining experience! :-)2012-11-05
  • 1
    Seriously, what have you tried? Drawing some pictures of different cases actually does help here.2012-11-05
  • 0
    I simply have no idea how to start answering it. I succeeded all my questions in my last homework and suddenly this question comes and I'm clueless.2012-11-05
  • 2
    Try this, let $\alpha = \sup A$. Then either $\alpha \in A$ or not. If it is you are finished. If not, use the property above to find a contradiction. Draw a picture. And take your vitamins.2012-11-05

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