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Any involution is a bijection.. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x ↦ −x), reciprocation (x ↦ 1/x), and complex conjugation (z ↦ z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the ...
Involutive negation (unary) can be added as an additional negation to t-norm logics whose residual negation is not itself involutive, that is, if it does not obey the law of double negation . A t-norm logic L {\displaystyle L} expanded with involutive negation is usually denoted by L ∼ {\displaystyle L_{\sim }} and called L {\displaystyle L ...
In a dagger category , a morphism is called . unitary if † =,; self-adjoint if † =.; The latter is only possible for an endomorphism:.The terms unitary and self-adjoint in the previous definition are taken from the category of Hilbert spaces, where the morphisms satisfying those properties are then unitary and self-adjoint in the usual sense.
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition to another proposition "not ", written , , ′ [1] or ¯. [citation needed] It is interpreted intuitively as being true when is false, and false when is true.
In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An involute of a curve is the locus of a point on a piece of taut string as the string is either unwrapped from or wrapped around the curve. [1] The evolute of an involute is the original curve.
In mathematics, a *-ring is a ring with a map * : A → A that is an antiautomorphism and an involution. More precisely, * is required to satisfy the following properties: [1] (x + y)* = x* + y* (x y)* = y* x* 1* = 1 (x*)* = x; for all x, y in A. This is also called an involutive ring, involutory ring, and ring with involution. The third axiom ...
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This definition, while terse and commonly used, is suboptimal for certain purposes because it contains an existential quantifier which is not really necessary. To avoid this, we may write the unique c ∈ R {\displaystyle c\in \mathrm {R} } such that a c = b {\displaystyle a\triangleleft c=b} as b a . {\displaystyle b\triangleright a.}