# Homework Help: Proof in set theory.

1. Oct 18, 2011

### mtayab1994

1. The problem statement, all variables and given/known data

{1/x+1/y / (x,y) in (IN*)^2} subset of ]0,2]

2. Relevant equations

3. The attempt at a solution

When x=y=1 u get a sum of 2 which is in ]0,2] and for any x and y greater than 1 u get a sum between 0<sum≤2.
It's a simple problem but i just don't know how to show the proof. Some help please.

2. Oct 18, 2011

### Staff: Mentor

What is this supposed to mean?

3. Oct 18, 2011

### micromass

Do you mean to say that

$$\{1/x+1/y~\vert~x,y\in \mathbb{N}\setminus\{0\}\}$$

That would make sense...

So you need to show that

$$\frac{1}{x}+\frac{1}{y}\leq 2$$

for all naturals x and y. Maybe use the fact that

$$\frac{1}{x+1}\leq \frac{1}{x}$$

and do induction??

4. Oct 19, 2011

### mtayab1994

Yep that's exactly what I wanted to say. thank you.