Is E a subset of ]0,2] and how does it relate to ]0,2]?

[Andrax]

we have E=(a+b)/ab (a,b)EN*
1/ prove that E C ]0,2] (i already duid that )
2/ is ]0,2] E E? shelp me in this one!

Homework Equations

The Attempt at a Solution

x $\in$ ]0,2] $\Rightarrow$ x $\in$ E

 

[LCKurtz]

we have E=(a+b)/ab (a,b)EN*
1/ prove that E C ]0,2] (i already duid that )
2/ is ]0,2] E E? shelp me in this one!

Homework Equations

The Attempt at a Solution

x $\in$ ]0,2] $\Rightarrow$ x $\in$ E

If E=(a+b)/ab what does EN* mean? What does ]0,2]E E mean? Please state your problem with proper notation.

 

[Mark44]

If E=(a+b)/ab what does EN* mean?

E means $\in$ and N* means the positive integers, I believe.

What does ]0,2]E E mean? Please state your problem with proper notation.

I second that.

 

[Andrax]

well sorry didn't find the proper notations in the advanced mode umm any solution?

 

[Mark44]

well sorry didn't find the proper notations in the advanced mode umm any solution?

You can use ε in the top row of Quick Symbols (on the right after you click Go Advanced). Or you can use LaTeX: [ itex ] \in [ /itex ] (without the spaces).

Also, tell us what you meant by N*.

 

[Ray Vickson]

well sorry didn't find the proper notations in the advanced mode umm any solution?

You could try using words:
E = {(a+b)/(ab): a,b positive integers}. And "is ]0,2] a subset of E?"
or
E = {(a+b)/(ab): a,b,in N*}, and "is ]0,2] subset E?"

RGV

 

[Andrax]

You could try using words:
E = {(a+b)/(ab): a,b positive integers}. And "is ]0,2] a subset of E?"
or
E = {(a+b)/(ab): a,b,in N*}, and "is ]0,2] subset E?"

RGV

I want to prove that ]0,2 is a subset of E E = {(a+b)/(ab): a,b,in N*}, and "is ]0,2] subset E?"

 

[LCKurtz]

Aren't all the numbers in E rational?

 

[HallsofIvy]

I want to prove that ]0,2 is a subset of E E = {(a+b)/(ab): a,b,in N*}, and "is ]0,2] subset E?"

In other words, you want to show that if $0< x\le 2$, the x= (a+ b)/(ab) for some positive integers a and b. $\sqrt{2}$ lies between 0 and 2 doesn't it?

 

[Andrax]

In other words, you want to show that if $0< x\le 2$, the x= (a+ b)/(ab) for some positive integers a and b. $\sqrt{2}$ lies between 0 and 2 doesn't it?

yes it does what's your point?

 

[Andrax]

ohh i get your point wow that's really easy don't know how i missed it