Simple Proof

  • #1

Homework Statement


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)?


Homework Equations





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!
 

Answers and Replies

  • #2
MathematicalPhysicist
Gold Member
4,309
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Just follow the definition.
The infiimum is the greatest number which is least than any other number in X.
 
  • #3
828
2
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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