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Math Help - analysis help

  1. #1
    Junior Member
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    analysis help

    Any ideas? Thanks!

    Let I be a bounded interval. Prove that the intersection of I and Z is a finite set.
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  2. #2
    Senior Member
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    Quote Originally Posted by friday616 View Post
    Any ideas? Thanks!

    Let I be a bounded interval. Prove that the intersection of I and Z is a finite set.
    Maybe I'm taking some theorems for granted, here, which you are not permitted to do. However, I would say simply, as follows:

    Since I is bounded, then so too is I\cap\mathbb{Z} bounded. Thus |I\cap\mathbb{Z}|=1+\sup(I\cap\mathbb{Z})-\inf (I\cap\mathbb{Z}).
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