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If a category is equivalent to the opposite (or dual) of another category then one speaks of a duality of categories, and says that the two categories are dually equivalent. An equivalence of categories consists of a functor between the involved categories, which is required to have an "inverse" functor.
In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent and consequent negated and swapped.
The most significant point of contact, however, between Eteocles and the suppliant Danaids is, in fact, their extreme positions with regard to the opposite sex: the misogyny of Eteocles' outburst against all women of whatever variety has its counterpart in the seeming misandry of the Danaids, who although opposed to their Egyptian cousins in ...
In category theory, a branch of mathematics, the opposite category or dual category C op of a given category C is formed by reversing the morphisms, i.e. interchanging the source and target of each morphism. Doing the reversal twice yields the original category, so the opposite of an opposite category is the original category itself.
Apples and oranges are both similar-sized seeded fruits that grow on trees, but that does not make the two interchangeable. A false equivalence or false equivalency is an informal fallacy in which an equivalence is drawn between two subjects based on flawed or false reasoning.
The inverse and the converse of a conditional are logically equivalent to each other, just as the conditional and its contrapositive are logically equivalent to each other. [1] But the inverse of a conditional cannot be inferred from the conditional itself (e.g., the conditional might be true while its inverse might be false [2]). For example ...
The Ten Commandments of Socialist Morality and Ethics (German: Zehn Gebote der sozialistischen Moral und Ethik), also known as Ten Commandments for the New Socialist Man (German: 10 Gebote für den neuen sozialistischen Menschen), were proclaimed by Walter Ulbricht, then First Secretary of the Socialist Unity Party of Germany (SED) in 1958. [2]
Formal equivalence is often more goal than reality, if only because one language may contain a word for a concept which has no direct equivalent in another language. In such cases, a more dynamic translation may be used or a neologism may be created in the target language to represent the concept (sometimes by borrowing a word from the source ...