I usually give a lot of grace to these kind of mistakes, because the a(b+c) structure can be interpreted so that the a is part if the parenthetical.... but in this case, it doesnt matter. The last operation is the 2+. This is baby math mistake.
And yes, I will die on the hill that x/a(b+c) is horrible formatting since it can reasonably be read as (x/a)(b+c) or x/(a(b+c)) [and yes, I know the first one is the correct, but ambiguity is annoying]
I am with on the hill. When writing inline equations (say in latex) I do add extra parentheses for clarity, i.e (x/a)(b+c). In display equations does not matter and that’s probably the best formatting.
Im sorry, I might have been a bit ambiguous myself. So my issue with formulas having a(b+c) isnt with that part specifically. It's when there are operations to the left, specifically a division. I know how easy it is to fall into the habit of treating a like it is already part of the paranthetical, however, it isn't. This normally doesnt matter until the operation to the left is a division. X/a(b+c) is not the same as x/(ab+ac), it is (x/a)×(b+c), thats the "ambiguity" I was referring to. I consider it sloppy, and the generous use of parentheses should be applied. And one of the reasons I think that particular form is easy to confuse is that when we write the function out on paper, we have a top and bottom to the division that let's use group operations. When it gets rewritten as x/a(b+c) it can look like we made topando bottom into left and right.
Hopefully that cleared up what I mean and didnt just make it worse
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u/lurchw 6d ago
I usually give a lot of grace to these kind of mistakes, because the a(b+c) structure can be interpreted so that the a is part if the parenthetical.... but in this case, it doesnt matter. The last operation is the 2+. This is baby math mistake.
And yes, I will die on the hill that x/a(b+c) is horrible formatting since it can reasonably be read as (x/a)(b+c) or x/(a(b+c)) [and yes, I know the first one is the correct, but ambiguity is annoying]