Proof in set theory.

  • Thread starter mtayab1994
  • Start date
  • #1
mtayab1994
584
0

Homework Statement



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

Homework Equations





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.
 

Answers and Replies

  • #2
36,335
8,293

Homework Statement



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

Homework Equations





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.
 
  • #3
micromass
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
22,178
3,305
Do you mean to say that

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

That would make sense...

So you need to show that

[tex]\frac{1}{x}+\frac{1}{y}\leq 2[/tex]

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

[tex]\frac{1}{x+1}\leq \frac{1}{x}[/tex]

and do induction??
 
  • #4
mtayab1994
584
0
Do you mean to say that

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

That would make sense...

So you need to show that

[tex]\frac{1}{x}+\frac{1}{y}\leq 2[/tex]

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

[tex]\frac{1}{x+1}\leq \frac{1}{x}[/tex]

and do induction??

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

Suggested for: Proof in set theory.

Replies
7
Views
365
Replies
12
Views
348
Replies
2
Views
308
Replies
2
Views
305
  • Last Post
Replies
4
Views
170
  • Last Post
Replies
10
Views
293
  • Last Post
Replies
3
Views
652
  • Last Post
Replies
20
Views
243
Replies
9
Views
291
  • Last Post
Replies
18
Views
438
Top