“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.
随便看	magnetic quiet zone magnetic reconnection magnetic recording magnetic residual loss magnetic resistance magnetic resonance magnetic resonance imaging magnetic sampling magnetic saturation magnetic screening magnetic separator magnetic shunt magnetic signature magnetic star magnetic storage magnetic storm magnetic stripe magnetic stripe card magnetic survey magnetic susceptibility magnetic tape magnetic tape cartridge magnetic tape unit transient variation transimpedance