# Thread: Can somebody point me in the right direction

1. ## Can somebody point me in the right direction

Hello,

I'm having abit of difficulty trying to figure out what needs to be done here, could somebody point in the right direction

Best

2. ## Re: Can somebody point me in the right direction

Originally Posted by entrepreneurforum.co.uk
Hello,
I'm having abit of difficulty trying to figure out what needs to be done here, could somebody point in the right direction
You are given ${J_n} = \left[ {0,1-\frac{1}{{n + 1}}} \right)$

For examples:
$J_1\cup J_2\cup J_3=\left[ {0,\frac{1}{{2}}} \right)\cup\left[ {0,\frac{2}{{3}}} \right)\cup\left[ {0,\frac{3}{{4}}} \right)=\left[ {0,\frac{3}{{4}}} \right)$

$J_1\cap J_2\cap J_3=\left[ {0,\frac{1}{{2}}} \right)\cap\left[ {0,\frac{2}{{3}}} \right)\cap\left[ {0,\frac{3}{{4}}} \right)=\left[ {0,\frac{1}{{2}}} \right)$

Now can you find $\bigcup\limits_{n = 1}^\infty {{J_n}} \,\& \,\bigcap\limits_{n = 1}^\infty {{J_n}}~?$

3. ## Re: Can somebody point me in the right direction

For the first one, which is the easiest, J1= (0, 1/1)= (0, 1) while I1= (0, 1- 1/2)= (0, 1/2). The "Difference", J1\I1= (1/2, 1). For n= 2, J2 (0, 1/2) while I2= (0, 1- 1/3)= (0, 2/3) so J2\I2 is empty.

4. ## Re: Can somebody point me in the right direction

Originally Posted by HallsofIvy
For the first one, which is the easiest, J1= (0, 1/1)= (0, 1) while I1= (0, 1- 1/2)= (0, 1/2). The "Difference", J1\I1= (1/2, 1). For n= 2, J2 (0, 1/2) while I2= (0, 1- 1/3)= (0, 2/3) so J2\I2 is empty.
Huh. I read it differently, and I get:

Jn\In = {0} U (1/n,n/(n+1)), except for J1\I1, for which I have {0}.