# −2
**−2** (negative two, minus two) is the integer that is the additive inverse of 2: the unique number that gives 0 when added to 2. It lies two units to the left of zero on the number line, is even, and is written with a minus sign preceding the digit 2.
| Key fact | Detail |
|---|---|
| Algebraic role | Additive inverse of 2; multiplying any number by −1 gives its opposite, so −1 · 2 = −2[1](https://openstax.org/books/elementary-algebra-2e/pages/1-4-multiply-and-divide-integers) |
| Order on the number line | −2 lies to the left of 0 and to the right of −6, so −6 < −2 < 0; the greater number is always the one farther right[2](https://openstax.org/books/contemporary-mathematics/pages/3-2-the-integers) |
| Sign rules | (−2) × (−5) = 10: the product of two negative numbers is positive, while (−2) × 5 = −10[1](https://openstax.org/books/elementary-algebra-2e/pages/1-4-multiply-and-divide-integers) |
| Computer representation | In two's-complement binary, the 3-bit pattern 110 denotes −2; an 8-bit signed integer holds values from −128 to +127[3](https://www.gnu.org/software/c-intro-and-ref/manual/html_node/Integer-Representations.html) |
| Notation | The preferred character is U+2212 MINUS SIGN, distinct from the hyphen-minus U+002D; a negative value is written with no space after the sign[4](https://www.stylemanual.gov.au/grammar-punctuation-and-conventions/numbers-and-measurements/mathematical-relationships) • [5](https://unicode.org/versions/Unicode18.0.0/core-spec/chapter-22/) |
| Historical status | Negative magnitudes were first accepted as numbers by medieval Indian mathematicians such as Brahmagupta (7th century) and Bhaskara (12th century); Western mathematics fully legitimized them only in the 19th century[6](https://egrove.olemiss.edu/aah_journal/vol25/iss2/9/) |
## Arithmetic properties
As an integer, −2 belongs to the set \( \{\dots, -3, -2, -1, 0, 1, 2, 3, \dots \} \), formed by extending the counting numbers with zero and the negatives[2](https://openstax.org/books/contemporary-mathematics/pages/3-2-the-integers). Its defining property is that \( -2 + 2 = 0 \): it is the additive inverse of 2, the number at the same distance from zero on the number line but in the opposite direction[1](https://openstax.org/books/elementary-algebra-2e/pages/1-4-multiply-and-divide-integers). Its absolute value, which measures distance from zero without regard to direction, is 2[2](https://openstax.org/books/contemporary-mathematics/pages/3-2-the-integers).
Comparison of negative integers follows position on the number line, not digit size. Since −2 is to the right of −6, −2 is the larger number, a point textbooks flag explicitly because learners often ignore signs and conclude that −6 exceeds −2[2](https://openstax.org/books/contemporary-mathematics/pages/3-2-the-integers).
The sign rules give −2 a consistent algebra. Adding a negative integer moves left on the number line, and subtracting a negative integer moves right, so \( 3 - (-2) = 5 \)[2](https://openstax.org/books/contemporary-mathematics/pages/3-2-the-integers). In multiplication and division, like signs give a positive result and unlike signs a negative one: \( (-2) \cdot (-5) = 10 \) and \( (-2) \cdot 5 = -10 \)[1](https://openstax.org/books/elementary-algebra-2e/pages/1-4-multiply-and-divide-integers). Multiplying by −1 is the same as taking the opposite, which is why \( -1 \cdot 2 = -2 \)[1](https://openstax.org/books/elementary-algebra-2e/pages/1-4-multiply-and-divide-integers).
## Notation
The horizontal stroke before the 2 is typographically distinct from a hyphen. The Unicode Standard encodes U+2212 MINUS SIGN as a mathematical operator and distinguishes it from the ASCII-derived U+002D HYPHEN-MINUS, which may look the same or be shorter[5](https://unicode.org/versions/Unicode18.0.0/core-spec/chapter-22/). Style guidance for mathematical writing is to show a negative value by writing the number immediately after the minus symbol without a space, since the sign modifies the number rather than operating on another quantity[4](https://www.stylemanual.gov.au/grammar-punctuation-and-conventions/numbers-and-measurements/mathematical-relationships). In handwriting and print the same symbol also serves as the subtraction operator, and algebra teaching notes that one symbol can carry different meanings, a source of learner difficulty[1](https://openstax.org/books/elementary-algebra-2e/pages/1-4-multiply-and-divide-integers).
## Representation in computing
Computers store signed integers such as −2 in two's-complement form, in which negation is computed by inverting the bits and adding one. In a 3-bit width, the pattern 110 represents −2, and the signed values run from −4 to 3[3](https://www.gnu.org/software/c-intro-and-ref/manual/html_node/Integer-Representations.html). An n-bit two's-complement signed integer ranges from \( -2^{n-1} \) to \( 2^{n-1} - 1 \), so an 8-bit integer holds −128 through +127[3](https://www.gnu.org/software/c-intro-and-ref/manual/html_node/Integer-Representations.html). A consequence of this scheme is that the most negative value lacks a positive counterpart, so negating it overflows and returns the same value[3](https://www.gnu.org/software/c-intro-and-ref/manual/html_node/Integer-Representations.html).
## Historical background
Negative quantities entered recorded mathematics in India and, according to some histories, earlier in China. The *Brahmasphutasiddhanta*, written by [Brahmagupta](https://www.edgepedia.org/brahmagupta) in 628 CE, contains systematic rules for arithmetic with positive and negative numbers and zero, treating positives as fortunes and negatives as debts[7](https://mathshistory.st-andrews.ac.uk/Biographies/Brahmagupta/) • [6](https://egrove.olemiss.edu/aah_journal/vol25/iss2/9/). The accounting historian Richard Mattessich, emeritus professor at the [University of British Columbia](https://www.edgepedia.org/university-of-british-columbia), argues that India's long accounting tradition, in which a debt is the inverse of an asset, conditioned this early acceptance of negative magnitudes as numbers[6](https://egrove.olemiss.edu/aah_journal/vol25/iss2/9/). Western mathematicians resisted legitimizing negative numbers for centuries, and the process was complete only in the 19th century[6](https://egrove.olemiss.edu/aah_journal/vol25/iss2/9/).
## Everyday and educational contexts
Negative numbers arise routinely in two everyday settings, money and temperature: a bank balance of −£30 records an overdraft of £30, and a forecast of −2°C means two degrees below freezing[8](https://www.open.edu/openlearn/mod/oucontent/view.php?id=81913§ion=1.2).
In mathematics education, small negative integers such as −2 are usually the first negatives learners meet, typically through the number line. Research shows that the difficulties persist beyond integers. A study of 94 pre-service primary teachers by Wanty Widjaja, Kaye Stacey, and Vicki Steinle of the [University of Melbourne](https://www.edgepedia.org/university-of-melbourne) identified two misconceptions in placing negative decimals on a number line: treating the positive and negative sides as separate rays aligned by context, and building the negative side by merging translated positive intervals. The authors conclude that teaching of negative numbers and the number line should not be confined to integers, as is frequently the case, but should also cover negative fractions and decimals[9](https://www.sciencedirect.com/science/article/pii/S0732312310000581).
## References
1. [Multiply and Divide Integers, OpenStax Elementary Algebra 2e](https://openstax.org/books/elementary-algebra-2e/pages/1-4-multiply-and-divide-integers)
2. [The Integers, OpenStax Contemporary Mathematics](https://openstax.org/books/contemporary-mathematics/pages/3-2-the-integers)
3. [Integer Representations, GNU C Language Manual](https://www.gnu.org/software/c-intro-and-ref/manual/html_node/Integer-Representations.html)
4. [Mathematical relationships, Australian Government Style Manual](https://www.stylemanual.gov.au/grammar-punctuation-and-conventions/numbers-and-measurements/mathematical-relationships)
5. [Chapter 22, The Unicode Standard Version 18.0.0](https://unicode.org/versions/Unicode18.0.0/core-spec/chapter-22/)
6. [Richard Mattessich (1998). From accounting to negative numbers: A signal contribution of medieval India to mathematics. Accounting Historians Journal 25(2).](https://egrove.olemiss.edu/aah_journal/vol25/iss2/9/)
7. [Brahmagupta (598–670), MacTutor History of Mathematics](https://mathshistory.st-andrews.ac.uk/Biographies/Brahmagupta/)
8. [Negative numbers, OpenLearn Everyday Maths 1, The Open University](https://www.open.edu/openlearn/mod/oucontent/view.php?id=81913§ion=1.2)
9. [Wanty Widjaja, Kaye Stacey, Vicki Steinle (2011). Locating negative decimals on the number line. Journal of Mathematical Behavior 30(1), 80–91.](https://www.sciencedirect.com/science/article/pii/S0732312310000581)
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*Topic: Encyclopedia › Physical world and mathematics › Mathematics and statistics › Numbers and algebra › Arithmetic and number systems › Number systems › Integers and rational numbers*
*Initially written Sep 17, 2026 · Reviewed: Sep 30, 2026; Oct 15, 2026 · Edited: Sep 30, 2026; Oct 15, 2026 · Last review: Oct 15, 2026*
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