# Simple Proof

1. Sep 22, 2011

### major_maths

1. The problem statement, all variables and given/known data
Let X={1/n: n$\in$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. Sep 22, 2011

### MathematicalPhysicist

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

3. Sep 22, 2011

### 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.