# Proof in set theory.

mtayab1994

## Homework Statement

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

## 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.

Mentor

## Homework Statement

{1/x+1/y / (x,y) in (IN*)^2} subset of ]0,2]
What is this supposed to mean?

## 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.

Staff Emeritus
Homework Helper
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??

mtayab1994
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??

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