Editing Negative number (section)

{{Short description|Real number that is strictly less than zero}}
{{Use dmy dates|date=December 2020}}
[[File:US Navy 070317-N-3642E-379 During the warmest part of the day, a thermometer outside of the Applied Physics Laboratory Ice Station's (APLIS) mess tent still does not break out of the sub-freezing temperatures.jpg|thumb|This thermometer is indicating a negative [[Fahrenheit]] temperature (−4&nbsp;°F).]]

In [[mathematics]], a '''negative number''' is the [[opposite (mathematics)|opposite]] of a positive [[real number]].<ref>"Integers are the set of whole numbers and their opposites.", Richard W. Fisher, No-Nonsense Algebra, 2nd Edition, Math Essentials, {{ISBN|978-0999443330}}</ref> Equivalently, a negative number is a real number that is [[inequality (mathematics)|less than]] [[0|zero]]. Negative numbers are often used to represent the [[Magnitude (mathematics)|magnitude]] of a loss or deficiency. A [[debt]] that is owed may be thought of as a negative asset. If a quantity, such as the charge on an electron, may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as ''positive'' and ''negative''. Negative numbers are used to describe values on a scale that goes below zero, such as the [[Celsius]] and [[Fahrenheit]] scales for temperature. The laws of arithmetic for negative numbers ensure that the common-sense idea of an opposite is reflected in arithmetic. For example, −{{px2}}(−3) = 3 because the opposite of an opposite is the original value.

Negative numbers are usually written with a [[Plus and minus signs|minus sign]] in front. For example, −3 represents a negative quantity with a magnitude of three, and is pronounced and read as "minus three" or "negative three". Conversely, a number that is greater than zero is called ''positive''; zero is usually ([[signed zero|but not always]]) thought of as neither positive nor [[negative zero|negative]].<ref>The convention that zero is neither positive nor negative is not universal. For example, in the French convention, zero is considered to be ''both'' positive and negative. The French words [[:fr:Nombre positif|positif]] and [[:fr:Nombre négatif|négatif]] mean the same as English "positive or zero" and "negative or zero" respectively.</ref> The positivity of a number may be emphasized by placing a plus sign before it, e.g. +3. In general, the negativity or positivity of a number is referred to as its [[sign (mathematics)|sign]].

Every real number other than zero is either positive or negative. The non-negative whole numbers are referred to as [[natural number]]s (i.e., 0, 1, 2, 3, ...), while the positive and negative whole numbers (together with zero) are referred to as [[integer]]s. (Some definitions of the natural numbers exclude zero.)

In [[bookkeeping]], amounts owed are often represented by red numbers, or a number in parentheses, as an alternative notation to represent negative numbers.

Negative numbers were used in the ''[[Nine Chapters on the Mathematical Art]]'', which in its present form dates from the period of the Chinese [[Han dynasty]] (202 BC – AD 220), but may well contain much older material.<ref name=struik33>Struik, pages 32–33. "In these matrices we find negative numbers, which appear here for the first time in history."</ref> [[Liu Hui]] (c. 3rd century) established rules for adding and subtracting negative numbers.<ref name="Hodgkin"/> By the 7th century, Indian mathematicians such as [[Brahmagupta]] were describing the use of negative numbers. [[Islamic mathematicians]] further developed the rules of subtracting and multiplying negative numbers and solved problems with negative [[coefficients]].<ref name=Rashed /> Prior to the concept of negative numbers, mathematicians such as [[Diophantus]] considered negative solutions to problems "false" and equations requiring negative solutions were described as absurd.<ref>[[Diophantus]], ''[[Arithmetica]]''.</ref> Western mathematicians like [[Gottfried Wilhelm Leibniz|Leibniz]] held that negative numbers were invalid, but still used them in calculations.<ref>{{cite book |last=Kline |first=Morris |date=1972 |title=Mathematical Thought from Ancient to Modern Times |publisher= Oxford University Press, New York |page= 252}}</ref><ref>{{cite web |url=https://web.ma.utexas.edu/users/mks/326K/Negnos.html |title=History of Negative Numbers |author-link=Martha K. Smith |first=Martha K. |last=Smith |publisher=[[University of Texas]] |date=February 19, 2001 |url-status=live |archive-url=https://web.archive.org/web/20250227120108/https://web.ma.utexas.edu/users/mks/326K/Negnos.html |archive-date=2025-02-27 |lang=en}}</ref>