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I am having a problem a finding a suitable formula for deciding whether a number falls inside of modular interval. Example:

Let's use $mod$ $100$ and the interval $\langle 90, 10\rangle$. How would you compute if the number $95$ or $0$ falls into the interval or not? In other words is there an expression that would be true for all the numbers in the interval?

John Smith
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  • If I have interpreted the term "wrapped" correctly, $\langle90,10\rangle$ is the same as $\langle -10,10\rangle$ which doesn't require any wrapping.

    Check whether the number modulo $100$ falls in this interval.

     – Guy Apr 07 '14 at 15:35
  • Is this what you want? If it is I'll upgrade that to an answer, I made it a comment because I wasn't sure. – Guy Apr 07 '14 at 15:36
  • @Sabyasachi Yeah you're right, I guess that's the right approach. Please make it an answer, and I'll gladly accept that. Thanks! – John Smith Apr 07 '14 at 15:42
  • Done.${}{}{}{}{}{}{}$ – Guy Apr 07 '14 at 15:46

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If I have interpreted the term "wrapped" correctly, $\langle90,10\rangle$ is the same as $\langle−10,10\rangle$ which doesn't require any wrapping. Check whether the number modulo $100$ falls in this interval.

Guy
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