Editing Subtraction (section)

{{Short description|One of the four basic arithmetic operations}}
{{Redirects|Subtract|other uses|Subtraction (disambiguation)}}
{{more citations needed|date=May 2018}}
[[File:Subtraction01.svg|thumb|"{{nowrap|5 − 2}} = 3" (verbally, "five minus two equals three")]]
{{Arithmetic operations}}
[[File:Shop placard showing 20% reduction.JPG|thumb|Placard outside a shop in [[Bordeaux]] advertising subtraction of 20% from the price of the second perfume purchased.]]
'''Subtraction''' (which is signified by the [[minus sign]], –) is one of the four [[Arithmetic#Arithmetic operations|arithmetic operations]] along with [[addition]], [[multiplication]] and [[Division (mathematics)|division]]. Subtraction is an operation that represents removal of objects from a collection.<ref>{{Cite web |title=What is to Subtract? |url=https://www.splashlearn.com/math-vocabulary/subtraction/subtract |access-date=2022-12-13 |website=SplashLearn|date=28 April 2022 }}</ref> For example, in the adjacent picture, there are {{nowrap|5 − 2}} peaches—meaning 5 peaches with 2 taken away, resulting in a total of 3 peaches. Therefore, the ''difference'' of 5 and 2 is 3; that is, {{nowrap|1=5 − 2 = 3}}. While primarily associated with natural numbers in [[arithmetic]], subtraction can also represent removing or decreasing physical and abstract quantities using different kinds of objects including [[negative number]]s, [[Fraction (mathematics)|fractions]], [[irrational number]]s, [[Euclidean vector|vectors]], decimals, functions, and matrices.<ref name=":0">{{Cite web|last=Weisstein|first=Eric W.|title=Subtraction|url=https://mathworld.wolfram.com/Subtraction.html|access-date=2020-08-26|website=mathworld.wolfram.com|language=en}}</ref>

In a sense, subtraction is the inverse of addition. That is, {{math|1=''c'' = ''a'' − ''b''}} [[if and only if]] {{math|1=''c'' + ''b'' = ''a''}}. In words: the difference of two numbers is the number that gives the first one when added to the second one.

Subtraction follows several important patterns. It is [[anticommutative]], meaning that changing the order changes the sign of the answer. It is also not [[associativity|associative]], meaning that when one subtracts more than two numbers, the order in which subtraction is performed matters. Because {{num|0}} is the [[additive identity]], subtraction of it does not change a number. Subtraction also obeys predictable rules concerning related operations, such as [[addition]] and [[multiplication]]. All of these rules can be [[mathematical proof|proven]], starting with the subtraction of [[integers]] and generalizing up through the [[real number]]s and beyond. General [[binary operations]] that follow these patterns are studied in [[abstract algebra]].

In [[computability theory]], considering subtraction is not [[Well-defined expression|well-defined]] over [[Natural number|natural numbers]], operations between numbers are actually defined using "truncated subtraction" or [[monus]].<ref>{{Cite book |last=Cutland |first=Nigel |title=Computability: an introduction to recursive function theory}}</ref>