merlan
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Let B_n = (0, \frac {1}{n} ] for all n \in N (N = set of natural numbers)
a) For each n \in N, find \bigcap _{k=1}^n B_k and \bigcup _{k=1}^n B_k
b) Find \bigcap _{n=1}^ \infty B_n and \bigcup _{n=1}^ \infty B_n
For a) I have
<br /> B_1 = (0,1] \\<br /> B_2 = (0, \frac {1}{2} ] \\<br /> B_3 = (0, \frac {1}{3} ]
so \bigcap _{k=1}^n B_k appears to be { \emptyset } and \bigcup _{k=1}^n B_k looks like (0,1]
I'm new to this and any help would be greatly appreciated. The questions I have are is a) correct? and what is the difference between a) and b)?
a) For each n \in N, find \bigcap _{k=1}^n B_k and \bigcup _{k=1}^n B_k
b) Find \bigcap _{n=1}^ \infty B_n and \bigcup _{n=1}^ \infty B_n
For a) I have
<br /> B_1 = (0,1] \\<br /> B_2 = (0, \frac {1}{2} ] \\<br /> B_3 = (0, \frac {1}{3} ]
so \bigcap _{k=1}^n B_k appears to be { \emptyset } and \bigcup _{k=1}^n B_k looks like (0,1]
I'm new to this and any help would be greatly appreciated. The questions I have are is a) correct? and what is the difference between a) and b)?