> In algebraic geometry we take the radical ideal sqrt(I) for an ideal I which is most certainly a set of values. But that's just overloaded syntax, isn't it?

> In algebraic geometry we take the radical ideal sqrt(I) for an ideal I which is most certainly a set of values. But that's just overloaded syntax, isn't it? We're concerned with real numbers here. > There is literally no reason we select the positive branch other than notational convenience Agreed, it's just a convention, though a very helpful one. > I've noticed some online resources recently are very careful about referring to sqrt(x) as the "principal square root function", something which is very good but that I have never once heard anyone say in real life, teacher or mathematician. I had to look up that one, since my maths education wasn't in English. I agree that it's nicer than what appears e.g. in my textbook: "the square root is always a positive number or zero", which conflicts wiwitthe definition that's on Wikipedia. It's probably the conflicting uses of "square root" to refer to two different things (all solutions, which is more relevant analytically, or the unique positive solution, which is more helpful for notation) that causes the kinds of freshman errors you mention. > You understand the concern here: simplifying notation masks the actual mathematics. My point is that it doesn't mask the actual mathematics any more than the regular notation already does. Which also is a problem, but not the one at hand.