Proof in set theory.

  • Thread starter mtayab1994
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  • #1
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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
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6,729

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
22,089
3,297
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
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.
 

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