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± vs ∓
When to use which
| Character | When to use it | Watch out for |
|---|---|---|
| ± Plus-minus Sign Plus-or-minus Sign | Two values at once, as in x = ±3, or a tolerance around a measurement, as in 5.7 ± 0.2. | Those are different claims. One says either of these, the other says somewhere in this range, and only context tells the reader which you meant. |
| ∓ Minus-or-plus Sign | Only ever alongside a ± in the same expression, to say take the opposite sign to that one. | Alone it means nothing at all. Flip one sign of a pair and not the other and the line still looks right while stating something false. |
One of these two signs cannot be used by itself. Write minus-or-plus on its own and it is inert — no value, no range, no choice offered — because everything it means is borrowed from a plus-minus somewhere else in the same expression. That dependency is the whole distinction between them, and it is why one of these characters is on every keyboard layout worth the name and the other is on none of them.
± is the busier sign, and it does two jobs that are easy to conflate. In x² = 9, therefore x = ±3, it means exactly one of these two values: the equation has two real roots and the sign is enumerating both. In a lab report, 5.7 ± 0.2 means nothing of the sort. That is a range — an admission of how far the measurement might be off — and there is no second answer hiding in it. Same glyph, and the distance between either and somewhere in here is left entirely to context.
∓ exists for a much narrower situation: an identity where two signs have to correspond in reverse. The angle-addition formula cos(a ± b) = cos a cos b ∓ sin a sin b is the standard example, folding two identities into a single line. Take the upper sign on the left and you are obliged to take the upper sign on the right. Without the minus-or-plus you write the sum case and the difference case out separately, which is twice the notation for the same content.
Because the signs are read as a pair — upper with upper, lower with lower — the failure mode is a quiet one. Change one and not the other and the expression remains well-formed, entirely legible, and false, with nothing about the line to suggest anything went wrong. It survives a proofread in a way that a missing bracket never does.
± has been part of computing much longer. It appears in Oughtred's Clavis Mathematicae in 1631, though appears in is the careful phrasing, since he used the sign rather than conjured it and the record of who put it on paper first is murkier than most sources admit. Unicode took the character wholesale from ISO 8859-1, where it sat at byte 0xB1, and that accident of inheritance is why it landed inside the first 256 codepoints and has been reliably typeable for decades: Option-Shift-= on a Mac, Alt+0177 on Windows, ± in HTML. ∓ has none of that. No mainstream layout offers it, LaTeX spells it \mp, and in running prose most writers give up and spell both cases out longhand — which is why the character is considerably rarer than the mathematics that calls for it.
Both signs have a life outside mathematics that borrows the pairing rather than the arithmetic. Chess annotation writes ± for a clear advantage to White and ∓ for the same advantage to Black, which is the correspondence idea applied to a notation with no addition in it anywhere. Everywhere else the practical rule is short: if you are writing a tolerance, ± and nothing else. If you are writing a pair of identities on one line, use both signs or use neither — a lone ∓ is not a stylistic choice, it is an unfinished sentence.