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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 ...
Pages in category "Articles with example Python (programming language) code" The following 200 pages are in this category, out of approximately 201 total. This list may not reflect recent changes. (previous page)
In C (and some other languages descended from C), double negation (!!x) is used as an idiom to convert x to a canonical Boolean, ie. an integer with a value of either 0 or 1 and no other. Although any integer other than 0 is logically true in C and 1 is not special in this regard, it is sometimes important to ensure that a canonical value is ...
Corner quotes, also called “Quine quotes”; for quasi-quotation, i.e. quoting specific context of unspecified (“variable”) expressions; [3] also used for denoting Gödel number; [4] for example “⌜G⌝” denotes the Gödel number of G. (Typographical note: although the quotes appears as a “pair” in unicode (231C and 231D), they ...
Loop-invariant code consists of statements or expressions that can be moved outside a loop body without affecting the program semantics. Such transformations, called loop-invariant code motion, are performed by some compilers to optimize programs. A loop-invariant code example (in the C programming language) is
Python supports a wide variety of string operations. Strings in Python are immutable, so a string operation such as a substitution of characters, that in other programming languages might alter the string in place, returns a new string in Python. Performance considerations sometimes push for using special techniques in programs that modify ...
It is frequently the case that antiautomorphisms are involutions, i.e. the square of the antiautomorphism is the identity map; these are also called involutive antiautomorphism s. For example, in any group the map that sends x to its inverse x −1 is an involutive antiautomorphism.