“trivial”的概念、定义、翻译、参考文献-科学参考

trivial

Mathematics

The term is used variously in mathematics. It may refer to the easiness of a conclusion. It also refers to simple or straightforward examples: the trivial group (or subgroup) consists only of the identity element; the trivial set is the empty set; the trivial subspace consists only of the zero vector; the trivial topology on a set consists only of the set itself and the empty set; the trivial factors of an integer n are ±1, ±n.

Logic

1. A property holding of a theory $T$ when $T$ proves every formula in its respective language, i.e., when $T$ is the language. For example, because classical logic is explosive, the deductive closure of the set ${p \land \neg p}$ is trivial. Because trivial theories are by definition complete, triviality is also known as over-completeness.
2. Describes a consequence relation $⊢$ (either syntactic or semantic) such that for all sets of formulae $Γ \cup {φ}$ drawn from its respective language, $Γ ⊢ φ$ holds, i.e., the trivial logic.

单词	trivial
释义	trivial Mathematics The term is used variously in mathematics. It may refer to the easiness of a conclusion. It also refers to simple or straightforward examples: the trivial group (or subgroup) consists only of the identity element; the trivial set is the empty set; the trivial subspace consists only of the zero vector; the trivial topology on a set consists only of the set itself and the empty set; the trivial factors of an integer n are ±1, ±n. Logic 1. A property holding of a theory $T$ when $T$ proves every formula in its respective language, i.e., when $T$ is the language. For example, because classical logic is explosive, the deductive closure of the set ${p \land \neg p}$ is trivial. Because trivial theories are by definition complete, triviality is also known as over-completeness. 2. Describes a consequence relation $⊢$ (either syntactic or semantic) such that for all sets of formulae $Γ \cup {φ}$ drawn from its respective language, $Γ ⊢ φ$ holds, i.e., the trivial logic.
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