13 Matching Annotations
1. Mar 2021
2. en.wikipedia.org en.wikipedia.org
1. In computer science, a tree is a widely used abstract data type that simulates a hierarchical tree structure

a tree (data structure) is the computer science analogue/dual to tree structure in mathematics

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3. en.wikipedia.org en.wikipedia.org
1. Model theory recognizes and is intimately concerned with a duality: it examines semantical elements (meaning and truth) by means of syntactical elements (formulas and proofs) of a corresponding language

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4. Jul 2020
5. en.wikipedia.org en.wikipedia.org
1. In logic, functions or relations A and B are considered dual if A(¬x) = ¬B(x), where ¬ is logical negation. The basic duality of this type is the duality of the ∃ and ∀ quantifiers in classical logic. These are dual because ∃x.¬P(x) and ¬∀x.P(x) are equivalent for all predicates P in classical logic
2. the ∧ and ∨ operators are dual in this sense, because (¬x ∧ ¬y) and ¬(x ∨ y) are equivalent. This means that for every theorem of classical logic there is an equivalent dual theorem. De Morgan's laws are examples

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6. May 2020
7. en.wikipedia.org en.wikipedia.org
1. Related concepts in other fields are: In natural language, the coordinating conjunction "and". In programming languages, the short-circuit and control structure. In set theory, intersection. In predicate logic, universal quantification.

Strictly speaking, are these examples of dualities (https://en.wikipedia.org/wiki/Duality_(mathematics))? Or can I only, at strongest, say they are analogous (a looser coonection)?

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8. en.wikipedia.org en.wikipedia.org

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9. en.wikipedia.org en.wikipedia.org
1. Mathematically speaking, necessity and sufficiency are dual to one another. For any statements S and N, the assertion that "N is necessary for S" is equivalent to the assertion that "S is sufficient for N".

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10. en.wikipedia.org en.wikipedia.org

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11. en.wikipedia.org en.wikipedia.org
1. This is an abstract form of De Morgan's laws, or of duality applied to lattices.

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12. en.wikipedia.org en.wikipedia.org
1. A plane graph is said to be self-dual if it is isomorphic to its dual graph.

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13. en.wikipedia.org en.wikipedia.org
1. In mathematical contexts, duality has numerous meanings[1] although it is "a very pervasive and important concept in (modern) mathematics"[2] and "an important general theme that has manifestations in almost every area of mathematics".[3]