Let $D_i := \{x \in \Bbb R: (-i \le x \le i)\} = [-i,i]$.
What does the notation for (i) mean?
$$(i)~ \bigcup_{i=1}^4 D_i, \quad(ii)~ \bigcap_{i=1}^4 D_i, \quad(iii)~ \bigcup_{i=1}^n D_i$$
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2$\begingroup$ Union of the sets $D_i$ where $i$ iterates from $1$ to $4$. Analogously for the others. In other words $(i)$ is the same as $D_1\cup D_2\cup D_3\cup D_4$ $\endgroup$– AlvinLCommented Nov 15, 2015 at 10:14
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$\begingroup$ thanks alvin, that's what I expected. $\endgroup$– Martin PfefferCommented Nov 15, 2015 at 10:15
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1 Answer
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$\bigcup_{i=1}^4 D_i = D_1 \cup D_2 \cup D_3 \cup D_4$.
This is analogous to $\sum_{i=1}^4 a_i = a_1 + a_2 + a_3 + a_4$, e.g.
$\bigcap_{i=1}^4 D_i = D_1 \cap D_2 \cap D_3 \cap D_4$, and the last one goes to $n$ (which is fixed for the sum), the $i$ is the running index that takes values $1$ to $n$.
answered Nov 15, 2015 at 10:17
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1$\begingroup$ Nice, thank you. I will accept your answer in a few mins (have to wait 10mins..) $\endgroup$ Commented Nov 15, 2015 at 10:19