Does inf(X) Exist and What is Its Value?

[major_maths]

Homework Statement

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)?

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!

 

[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.