I came across $$ x \in \bigcup\limits_{i=1}^\infty A_i $$ and some other notations similar to this one. I wonder if i can use this notation, let's say for intervals, for example $$ x \in \bigcup\limits_{k \in \mathbb Z} \left[2k\pi-\frac{7\pi}{6},2k\pi+\frac{\pi}{6}\right]$$ is the set of solutions of $ \sin(x) \le \frac{1}{2} $.
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Absolutely! This is even what is typically done. – Xander Henderson Sep 12 '17 at 14:24
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Many books use this notation, so don't sweat over it – AspiringMathematician Sep 12 '17 at 14:26
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Thank you guys for your responses. That really helped me. – mxaxc Sep 12 '17 at 14:28