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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 ...
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.
The map that sends x to x −1 is an example of a group antiautomorphism. Another important example is the transpose operation in linear algebra , which takes row vectors to column vectors . Any vector-matrix equation may be transposed to an equivalent equation where the order of the factors is reversed.
So, when the Washington, D.C. math teacher heard her daughter's alarm clock continue to ring one morning, she didn't think anything of it. Isabel Nugent at the beach.
Some cats are just complete velcro kitties — yes, we’re looking at you, Miss Siamese! These high-maintenance cat breeds can’t imagine being separated from their humans or missing out on any ...
One’s biological age, which measures the body’s physiological state, may help predict who is at risk for developing colon polyps, a known risk factor for colorectal cancer.
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