I am confused with the imagining the regions of $4$-dimensional space. I know that this space defines $2^4=16$ regions. Consider half upper space ($8$ regions). so $(2,3,4,1)$ belongs to the first region ($R_1$) and $(-2,3,4,1)\in R_2$. what we can say about other regions? for example $(-2,3,-4,1)\in R_?$ I wonder if anyone can spot a way to explain this for me?
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1Any sequence $(s_1,s_2,s_3,s_4)$ of signs $s_i\in{-,+}$ describes a region (and there are $2^4$ of them), so $(-2,3,-4,1)$ would belong to region $(-,+,-,+)$... – fweth Sep 22 '17 at 11:04
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If I want to counter it, what is it number? – C.F.G Sep 22 '17 at 11:22
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Is it a ordered set? – C.F.G Sep 22 '17 at 11:23
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1You can order it in many interesting ways! Lexicographic order would be the first choice, probably... – fweth Sep 22 '17 at 11:31