# Can somebody point me in the right direction

• Sep 11th 2013, 11:37 AM
entrepreneurforum.co.uk
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
• Sep 11th 2013, 12:24 PM
Plato
Re: Can somebody point me in the right direction
Quote:

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 $\bigcup\limits_{n = 1}^\infty {{J_n}} \,\& \,\bigcap\limits_{n = 1}^\infty {{J_n}}~?$
• Sep 11th 2013, 03:58 PM
HallsofIvy
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.
• Sep 12th 2013, 05:53 AM
Deveno
Re: Can somebody point me in the right direction
Quote:

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}.