# theorem 中文解釋 wordnet sense Collocation Usage Collins Definition
Noun
/ˈTHēərəm/,/ˈTHi(ə)r-/, Font size:  theorems, plural;
1. A general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths

2. A rule in algebra or other branches of mathematics expressed by symbols or formulae

1. a proposition deducible from basic postulates
2. an idea accepted as a demonstrable truth
3. In mathematics, a theorem is a statement which has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms. ...
4. Teorema (1968) is an Italian language movie directed by Pier Paolo Pasolini and starring Laura Betti, Silvana Mangano, Massimo Girotti, Terence Stamp, and Anne Wiazemsky. It was the first time Pasolini worked primarily with professional actors. ...
5. A mathematical statement of some importance that has been proven to be true. Minor theorems are often called propositions. ...
6. Any axiomatizable fuzzy theory is recursively enumerable. In particular, the fuzzy set of logically true formulas is recursively enumerable in spite of the fact that the crisp set of valid formulas is not recursively enumerable, in general. ...
7. A statement in a formal system that has proof.
8. If P is deducible from the empty set, we write |-T P , and say that P is a theorem or P is provable in T.
9. A main result. Usually the proof is somewhat involved and the result is interesting and useful. Constructive Proof
10. A nonnegative matrix A is irreducible if and only if, for any vector x>0 it is the case that A*x>0.
11. a formula or statement that is proven by other formulas
12. If for every point p in a neighborhood U of M, there exists a choice of gauge such that the change in an arbitrary length at p under congruent displacement to an infinitesimally near point q is given by
13. a generalization that must be proven before being accepted as true
14. A proposition that can be deduced from the premises of a system.
15. A statement that can be proven using logical (deductive) reasoning
16. Defining a set by is contradictory.
17. A wff that is proved or provable. Axioms are special cases of theorems. Notation: A (A is a theorem); or SA (A is a theorem in system S). See antitheorem; proof.
18. The following convergence–divergence test holds.