Minus-Plus Sign — Definition, Formula & Examples
The minus-plus sign (∓) is a mathematical symbol that means 'minus or plus,' indicating that when a companion ± is read as plus, the ∓ is read as minus, and vice versa.
The symbol ∓ denotes a composite operation whose sign is always opposite to that of a corresponding ± in the same expression. When ± takes the upper sign (+), ∓ takes the lower sign (−), and when ± takes the lower sign (−), ∓ takes the upper sign (+).
Key Formula
Where:
- = Plus-or-minus: take + in the first reading, − in the second
- = Minus-or-plus: take the opposite sign of ± in each reading
How It Works
The minus-plus sign never appears alone — it always accompanies a ± in the same expression. The two symbols are linked: you read the top signs together and the bottom signs together. For example, in , the two readings are and . This pairing lets you write two related equations in a single compact line.
Worked Example
Problem: Expand the expression into its two separate equations.
Reading 1 (upper signs): Replace ± with + and ∓ with −.
Reading 2 (lower signs): Replace ± with − and ∓ with +.
Answer: The single line with ± and ∓ encodes both the cosine addition and cosine subtraction identities.
Why It Matters
Trigonometric identities, quadratic-type formulas, and physics equations often package two mirror-image results into one line using ± and ∓ together. Recognizing ∓ lets you correctly unpack both equations without confusing the signs.
Common Mistakes
Mistake: Treating ∓ as independent from ±, choosing signs for each symbol separately.
Correction: The two symbols are always linked. When ± is +, ∓ must be −, and when ± is −, ∓ must be +. They never take the same sign in the same reading.