In mathematics, the additive inverse of an element x , denoted -x , is the element that when added to x , yields the additive identity , 0 . In the most familiar cases, this is the number 0, but it can also refer to a more generalized zero element .
12-460: (Redirected from Inverted ) [REDACTED] Look up inverse in Wiktionary, the free dictionary. Inverse or invert may refer to: Science and mathematics [ edit ] Inverse (logic) , a type of conditional sentence which is an immediate inference made from another conditional sentence Additive inverse (negation), the inverse of
24-538: A given number yields the multiplicative identity, 1 Inverse matrix of an Invertible matrix Other uses [ edit ] Invert level , the base interior level of a pipe, trench or tunnel Inverse (website) , an online magazine An outdated term for an LGBT person; see Sexual inversion (sexology) See also [ edit ] Inversion (disambiguation) Inverter (disambiguation) Opposite (disambiguation) Reverse (disambiguation) Complement (disambiguation) Topics referred to by
36-538: A given number yields the multiplicative identity, 1 Inverse matrix of an Invertible matrix Other uses [ edit ] Invert level , the base interior level of a pipe, trench or tunnel Inverse (website) , an online magazine An outdated term for an LGBT person; see Sexual inversion (sexology) See also [ edit ] Inversion (disambiguation) Inverter (disambiguation) Opposite (disambiguation) Reverse (disambiguation) Complement (disambiguation) Topics referred to by
48-414: A number that, when added to the original number, yields zero Compositional inverse , a function that "reverses" another function Inverse element Inverse function , a function that "reverses" another function Generalized inverse , a matrix that has some properties of the inverse matrix but not necessarily all of them Multiplicative inverse (reciprocal), a number which when multiplied by
60-478: Is different from Wikidata All article disambiguation pages All disambiguation pages inverse [REDACTED] Look up inverse in Wiktionary, the free dictionary. Inverse or invert may refer to: Science and mathematics [ edit ] Inverse (logic) , a type of conditional sentence which is an immediate inference made from another conditional sentence Additive inverse (negation),
72-400: Is different from Wikidata All article disambiguation pages All disambiguation pages Additive inverse In elementary mathematics , the additive inverse is often referred to as the opposite number. The concept is closely related to subtraction and is important in solving algebraic equations . Not all sets where addition is defined have an additive inverse, such as
84-445: Is typically only used to refer to a commutative operation, but it is not necessarily associative . When it is associative, so ( a + b ) + c = a + ( b + c ) {\displaystyle (a+b)+c=a+(b+c)} , the left and right inverses, if they exist, will agree, and the additive inverse will be unique. In non-associative cases, the left and right inverses may disagree, and in these cases,
96-400: The natural numbers . When working with integers , rational numbers , real numbers , and complex numbers , the additive inverse of any number can be found by multiplying it by −1 . The concept can also be extended to algebraic expressions, which is often used when balancing equations . The additive inverse is closely related to subtraction , which can be viewed as an addition using
108-429: The inverse of a number that, when added to the original number, yields zero Compositional inverse , a function that "reverses" another function Inverse element Inverse function , a function that "reverses" another function Generalized inverse , a matrix that has some properties of the inverse matrix but not necessarily all of them Multiplicative inverse (reciprocal), a number which when multiplied by
120-1026: The inverse: Conversely, the additive inverse can be thought of as subtraction from zero: This connection lead to the minus sign being used for both opposite magnitudes and subtraction as far back as the 17th century. While this notation is standard today, it was met with opposition at the time, as some mathematicians felt it could be unclear and lead to errors. Given an algebraic structure defined under addition ( S , + ) {\displaystyle (S,+)} with an additive identity e ∈ S {\displaystyle e\in S} , an element x ∈ S {\displaystyle x\in S} has an additive inverse y {\displaystyle y} if and only if y ∈ S {\displaystyle y\in S} , x + y = e {\displaystyle x+y=e} , and y + x = e {\displaystyle y+x=e} . Addition
132-411: The same term [REDACTED] This disambiguation page lists articles associated with the title Inverse . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Inverse&oldid=1029795415 " Category : Disambiguation pages Hidden categories: Short description
SECTION 10
#1732880752041144-411: The same term [REDACTED] This disambiguation page lists articles associated with the title Inverse . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Inverse&oldid=1029795415 " Category : Disambiguation pages Hidden categories: Short description
#40959