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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 ...
In this example, a self-adjoint morphism is a symmetric relation. The category Cob of cobordisms is a dagger compact category , in particular it possesses a dagger structure. The category Hilb of Hilbert spaces also possesses a dagger structure: Given a bounded linear map f : A → B {\displaystyle f:A\rightarrow B} , the map f † : B → A ...
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.
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 ...
As a further example, negation can be defined in terms of NAND and can also be defined in terms of NOR. Algebraically, classical negation corresponds to complementation in a Boolean algebra, and intuitionistic negation to pseudocomplementation in a Heyting algebra. These algebras provide a semantics for classical and intuitionistic logic.
In 1942, Mituhisa Takasaki (高崎光久) introduced an algebraic structure which he called a kei , [1] [2] which would later come to be known as an involutive quandle. [3] His motivation was to find a nonassociative algebraic structure to capture the notion of a reflection in the context of finite geometry .
A formula editor is a computer program that is used to typeset mathematical formulas and mathematical expressions. Formula editors typically serve two purposes: They allow word processing and publication of technical content either for print publication, or to generate raster images for web pages or screen presentations.
An unpublished computational program written in Pascal called Abra inspired this open-source software. Abra was originally designed for physicists to compute problems present in quantum mechanics. Kespers Peeters then decided to write a similar program in C computing language rather than Pascal, which he renamed Cadabra. However, Cadabra has ...