[johnrmead]

It might be nitpicking, but another issue that pops up in some high school courses is the 0<x<1 notation. One could argue that it’s an abuse of notation, but it is common enough that at least some students will come across it sooner or later. In this setting, the preferred reading might be that x is between 0 and 1, a statement which completely omits any mention of “greater than” or “less than”. It has always struck me as imprecise when I’ve told students that “<” means “less than”. I would much prefer to call both signs order symbols and instruct that “4<6” could be read “four is less than six” or “six is greater than four”.

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