It dawned on me a couple of weeks ago that I had no idea what terminology was used for the sets $[0,\infty)^n\subseteq \mathbb{R}^n$ in general. In one dimension, it's just the half line; in two dimensions, it's a quadrant; in three dimensions, it's an octant. After that I am at a loss. Is there a name for these sets in general?
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I think people tend to call it an "octant". – David C. Ullrich Apr 24 '16 at 18:08
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Well that's unsettling haha. – Cameron Williams Apr 24 '16 at 18:09
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6The positive/non-negative orthant. – Andrew D. Hwang Apr 24 '16 at 18:10
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Sorry - let's hope I'm wrong... – David C. Ullrich Apr 24 '16 at 18:10
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@AndrewD.Hwang Hah that's it! You should make that an answer. – Cameron Williams Apr 24 '16 at 18:11
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Mimicing the manifold terminology, maybe let's call it a... corner? – Santiago Apr 24 '16 at 18:14
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It's often called the positive (if open) or non-negative (if closed) orthant.
Andrew D. Hwang
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Thanks! It has been bothering me for a couple of weeks. It is surprising that this terminology doesn't come up in basic courses and (seemingly) isn't that popular. – Cameron Williams Apr 24 '16 at 18:31
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You're very welcome! It does seem like the sort of term one hears relatively rarely, and then only in scattered fields, such as toric geometry. – Andrew D. Hwang Apr 24 '16 at 18:41