In algebra, a minus sign is usually thought of as representing the operation of additive inverse ( sometimes called " negation " ), with the additive inverse of a positive number being negative and the additive inverse of a negative number being positive.
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In algebra, a minus sign is usually thought of as representing the operation of additive inverse ( sometimes called " negation " ), with the additive inverse of a positive number being negative and the additive inverse of a negative number being positive.
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This defines a form with desirable properties for vector spaces over fields of characteristic not equal to 2, but in a vector space over a field of characteristic 2, the definition is equivalent to that of a symmetric form, as every element is its own additive inverse.
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If one does not require a ring to have a unit, then one has to add the requirement of continuity of the additive inverse, or equivalently, to define the topological ring as a ring which is a topological group ( for + ) in which multiplication is continuous, too.
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In conjunction with a formula that defines the additive inverse of a real number in \ mathcal { R }, one can use \ varphi to define the usual ordering in \ mathcal { R } : for a, b \ in \ R, set a \ le b if and only if b-a is nonnegative.
