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Simple Proof

  1. Sep 22, 2011 #1
    1. The problem statement, all variables and given/known data
    Let X={1/n: n[itex]\in[/itex]N} (where N is the set of natural numbers)
    i) Does inf(X) exist?
    ii) What is inf(X)?

    2. Relevant equations

    3. The attempt at a solution
    I think I should try to prove inf(X) exists by considering it a Lower Limit, but I don't know how to go about doing that. Any help would be appreciated!
  2. jcsd
  3. Sep 22, 2011 #2


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    Gold Member

    Just follow the definition.
    The infiimum is the greatest number which is least than any other number in X.
  4. Sep 22, 2011 #3
    Well, surely you can guess at what the inf might be, right? Let's say you think that x is the inf. Now, just show that x is a lower bound and if y is bigger than x, then y isn't lower bound.
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