How to prove that infimum of $A = \{\frac{n}{2^n} : n \in N\}$ is 0?

Question

How to prove that infimum of $A = \{\frac{n}{2^n} : n \in N\}$ is 0?

Could you explain this to me step by step?

Answer 1

This set definitely admits an infimum. The only sets without an infimum are the one that do not admit any lower bound. This one is bounded below by $0$ so an infimum exists.