# Math Help - Archimedean property help

1. ## Archimedean property help

Q: If y is in R, y>0, then there is a positive integer n such that 1/n<y.

A: All I can think of is to use the fact that N is unbounded, thus for any value of y I can creat a smaller fraction with a larger value of n.

Also,

Q: Consider the set A={1/n : n is in R}. Prove that inf(A)=0.

Any help understanding how to do these would be much appreciated. Thank you.

2. Originally Posted by Danneedshelp
Q: If y is in R, y>0, then there is a positive integer n such that 1/n<y.

A: All I can think of is to use the fact that N is unbounded, thus for any value of y I can creat a smaller fraction with a larger value of n.
Try and be a bit more formal here.

Suppose $\exists \ y \in \mathbb{R} \ y>0 \ | \ \forall \ n \in \mathbb{N} \ \frac{1}{n} > y \ \implies \ \frac{1}{y} > n \ \forall \ n \in \mathbb{N}$ then some comment about the contradiction there would be nice.

Bobak