- #1

- 301

- 4

## Homework Statement

Prove that if a>0, there exists n in N such that 1/n < a < n.

## Homework Equations

## The Attempt at a Solution

I am starting with a>0 and trying to manipulate, algebraically, to get n > a > 1/n.

From a > 0 I can add 1 to both sides to obtain, a+1 > 1. Then I can choose some n such that:

n > a+1 > 1.

From there, divide by n to achieve the desired result for one part of the inequality:

1> (a+1)/n > 1/n. We know from above that n > 1, so I can write:

n > (a+1)/n > 1/n.

From here I'm not sure what to do.