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Oh, and “convex”. As far as convex sets go, the mathematical usage accords well with everyday language. Not so with convex (and concave) functions. Educationists (?) have tried to remedy this by using terms “concave up” and “concave down” in calculus textbooks, a usage that I detest. (I have a hard time remembering which is which of those two.)

Edited based on comments: It seems that in Russian, "convex" can refer a surface curved outward, where in English usually "convex" refers to a solid whose surface curves outward. Perhaps that's why in complex geometry, one might consider a "convex domain" or its boundary, a "convex hypersurface".

show/hide this revision's text 2 Convex up/down → concave up/down

Oh, and “convex”. As far as convex sets go, the mathematical usage accords well with everyday language. Not so with convex (and concave) functions. Educationists (?) have tried to remedy this by using terms “convex concave up” and “convex concave down” in calculus textbooks, a usage that I detest. (I have a hard time remembering which is which of those two.)

show/hide this revision's text 1 [made Community Wiki]

Oh, and “convex”. As far as convex sets go, the mathematical usage accords well with everyday language. Not so with convex (and concave) functions. Educationists (?) have tried to remedy this by using terms “convex up” and “convex down” in calculus textbooks, a usage that I detest. (I have a hard time remembering which is which of those two.)