Let [tex]B_n = (0, \frac {1}{n} ][/tex] for all [tex]n \in N [/tex] (N = set of natural numbers)(adsbygoogle = window.adsbygoogle || []).push({});

a) For each [tex]n \in N[/tex], find [tex] \bigcap _{k=1}^n B_k[/tex] and [tex] \bigcup _{k=1}^n B_k[/tex]

b) Find [tex] \bigcap _{n=1}^ \infty B_n[/tex] and [tex] \bigcup _{n=1}^ \infty B_n[/tex]

For a) I have

[tex]

B_1 = (0,1] \\

B_2 = (0, \frac {1}{2} ] \\

B_3 = (0, \frac {1}{3} ] [/tex]

so [tex] \bigcap _{k=1}^n B_k[/tex] appears to be [tex]{ \emptyset } [/tex] and [tex] \bigcup _{k=1}^n B_k[/tex] looks like [tex](0,1][/tex]

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)?

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# Homework Help: Indexed Families of Sets

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