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Possible Duplicate:
Why does “convex function” mean “concave up”?

Forty years ago I recall seeing the definition of a convex function (ie, that the points on the line segment joining two points on its graph are above its graph), with the definition of a concave function being that its negative is convex. Now, teaching high school mathematics, I am seeing “concave up” used with the meaning of “convex”, and “concave down” to mean “concave”. I can sympathize with the strong intuitive basis of this high school terminology, but I was just wondering whether is goes beyond high school. For example, when you are “really” doing mathematics, you speak of, say, the concavity of the logarithm, right?, never its “concave-down-ness”, right?

added just before posting: I see that T.. has pretty much answered this already here on MSE at a related post. Here’s the link:

Why does "convex function" mean "concave *up*"?

If you all want to close this question of mine as a duplicate, I won’t mind.

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    In the situations where I've come across them it's been more common to talk about convex functions than concave ones, probably because you talk about convex sets often, but never concave ones (since all "concave set" could possibly mean is "complement of a concave set").2011-09-28
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    I learned the *concave up/down* terminology over forty years ago, before I ever heard of a convex function. For almost forty years I’ve taught it in first-year university calculus; students have relatively little difficulty understanding it. I’m perfectly happy to omit *convex function* at that level: in my experience most calculus students will never need the terminology.2011-09-28
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    I also learned it before ever hearing of convex functions. Although I haven't had the problem myself, I can readily believe that some people might have a hard time remembering which is which if they were called simply "concave" and "convex" in first-year calculus.2011-09-28
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    I don't mind the question being closed, but I do not think it is accurate to call it an exact duplicate. The other question was only asking for help in understanding the terminology, whereas I was questioning the propriety of the terminology:)2011-09-29

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