The plus sign (+) and minus sign (−) are typographic symbols used primarily in mathematics, science, engineering, and everyday notation to denote addition, positive values, subtraction, and negative values, respectively.
Symbol Description
- Plus sign (+): Consists of a vertical stroke intersecting a horizontal stroke at their midpoints. In Unicode it is U+002B.
- Minus sign (−): A horizontal line of length slightly longer than a hyphen but shorter than an en dash. In Unicode it is U+2212. The hyphen-minus (‑) at U+002D is often used as a substitute in plain‑text contexts, though it is typographically distinct from the true minus sign.
Historical Development
- The plus sign originates from the Latin word et (“and”), which was abbreviated as a ligature resembling ⊕; over time this evolved into the modern plus shape by the 14th century.
- The minus sign developed from a simple horizontal line used to indicate subtraction or a negative quantity. Its use became standardized in European algebraic notation during the 16th and 17th centuries.
Mathematical Usage
- Addition: The expression a + b indicates the sum of a and b.
- Positive Numbers: A leading plus sign (e.g., +5) explicitly marks a number as positive, though it is often omitted in practice.
- Subtraction: The expression a − b denotes the difference between a and b.
- Negative Numbers: A leading minus sign (e.g., −3) designates a number less than zero.
Scientific and Engineering Contexts
- Electrical Engineering: The plus and minus signs denote polarity of terminals and voltage signs.
- Chemistry: They indicate oxidation states (e.g., Fe³⁺, Cl⁻) and ionic charges.
- Physics: They are used for vector components, charge signs, and directionality in equations.
Typography and Encoding
- In well‑formatted typeset material, the minus sign (U+2212) is preferred over the hyphen‑minus to maintain proper spacing and visual distinction.
- The plus sign is consistently rendered as a centered cross, while the minus sign is rendered as a centered horizontal line.
Computing and Programming
- Most programming languages employ the ASCII plus (+) and hyphen‑minus (‑) characters for addition and subtraction operations.
- Specialized mathematical software often substitutes the Unicode minus sign for improved readability in displayed formulas.
Cultural and Miscellaneous Usage
- The plus sign is employed in informal contexts to indicate approval, positivity, or inclusion (e.g., “cross‑plus” in voting).
- The minus sign can convey negation or a reduction in non‑numeric contexts (e.g., “minus the usual fanfare”).
References
- Unicode Consortium, “Unicode Standard, Version 15.0,” 2022.
- Cajori, Florian. A History of Mathematical Notations. Open Court Publishing, 1929.
- Ifrah, Georges. The Universal History of Numbers. John Wiley & Sons, 2000.
