Simple Proof

major_maths

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!

MathematicalPhysicist

Just follow the definition.
The infiimum is the greatest number which is least than any other number in X.

Robert1986

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.