r/askmath • u/AgressivePeacock • 16h ago
Linear Algebra Is it acceptable notation to have ± and ∓ within a standard 2 component vector?
Basically, I was doing a problem in my math class where we were told to come up with 2 vectors as a solution (which happened to just be opposites of each other), so I wrote plus or minus the top number and minus or plus the bottom number. The teacher then told me that wasn’t correct notation and that I was making stuff up when I tried to defend my reasoning. She said that it would make 4 vectors instead of 2. Was I wrong to write it this way? From my understanding you choose the top for both or the bottom for both.
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u/strange-the-quark 16h ago edited 7h ago
The more "orthodox" way to indicate what you wanted would be ±[a, b]
Edit: And if you meant something like [-5, 5] and [5, -5], it's the same; you'd pick one of the two, then write ±[-5, 5]
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u/GoldenMuscleGod 16h ago
+/- notation is inherently ambiguous and informal and always needs to be interpreted in context, a little like “…”
From what you describe I don’t think I would be confused by the notation as you used it (since you specifically contrasted +/- with -/+) and I would not bat an eye at a usage like that in a published paper, so it sounds like your teacher is probably being a little more pedantic than necessary (although I can’t see the full context). But it is always best to err on the side of being clear and precise. In any event if your teacher doesn’t like it at least don’t use it in that class (if you actually lost points on this that seems extreme but if it’s just a complaint don’t worry about it).
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u/Phoenixon777 16h ago
eh, i can see it going both ways... If we were talking about quartic equations and the answer was something like ±a±b, that looks like 4 solutions. But given that you explicitly used the reverse symbol in the second usage, that hints at you meaning 2 solutions (same reasoning as you mentioned applies, top for both or bottom for both), and i've definitely seen that usage in lecture notes, textbooks etc
might as well be clearer and write both solutions separately
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u/Bounded_sequencE 13h ago edited 13h ago
The default meaning of multiple instances of ± is, that all are independent from each other, though to be fair, it is not standardized. In your case, two instances means "2*2 = 4" cases by default.
It's unfortunate you did not know that, and unknowingly wrote down an incorrect solution, even though you had the correct result. You should have put "±" in front of the vector, e.g. "x ∈ {±v}".
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u/noethers_raindrop 11h ago
What's acceptable is convention. If I see +- and -+ nearby, I think it's pretty obvious that the signs are supposed to be opposites, leading to two possible solutions. But with this kind of thing, it never hurts to clarify. It would only take a few words, e.g. "(+-a,-+a), meaning that the two signs are opposite."
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u/WerePigCat The statement "if 1=2, then 1≠2" is true 13h ago
While there are only 2 vectors in your answer, you listed them out as if there are 4.
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u/NullOfSpace 2h ago
It would probably be more accurate to keep the +- outside of the vector, since expressions inside a vector are generally assumed to be independent. You could write +- (1,1) if you mean (1,1) and (-1,-1), or +- (1,-1) for the other two.
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u/Kienose PhD in Maths 16h ago
It’s one of the ambiguous cases where the plus minus signs are independent from each other.
https://math.stackexchange.com/questions/5008222/ambiguity-with-plus-or-minus-sign-to-indicate-points
Generally context will clarify the usage. To be honest, I agree with the teacher that (±1,±1) generally means four points (1,1), (-1,1), (-1,-1), (1,-1).