一切由lemma来：http://www.etthink.com/thread-283231-1-1.html
(1) Definition（定义）------a precise and unambiguous description of the meaning of a mathematical term. It characterizes the meaning of a word by giving all the properties and only those properties that must be true.
(2) Theorem（定理）----a mathematical statement that is proved using rigorous mathemat-ical reasoning. In a mathematical paper, the term theorem is often reserved for the most important results.
(3) Lemma（引理）----a minor result whose sole purpose is to help in proving a theorem. It is a stepping stone on the path to proving a theorem. Very occasionally lemmas can take on a life of their own (Zorn’s lemma, Urysohn’s lemma, Burnside’s lemma,Sperner’s lemma).
(4) Corollary（推论）-----a result in which the (usually short) proof relies heavily on a given theorem (we often say that\this is a corollary of Theorem A").
conclude
(5) Proposition（命题）-----a proved and often interesting result, but generally less important than a theorem.
(6) Conjecture（推测，猜想）----a statement that is unproved, but is believed to be true (Collatz conjecture, Goldbach conjecture, twin prime conjecture).
(7) Claim（断言）-----an assertion that is then proved. It is often used like an informal lemma.
(8) Axiom/Postulate------（公理/假定）a statement that is assumed to be true without proof. These are the basic building blocks from which all theorems are proved (Eu-clid’s ve postulates, Zermelo-Frankel axioms, Peano axioms).
axiom
英 [ˈæksiəm] 美 [ˈæksiəm]
For if there were infinitely many axioms, they could not all be written out.
因为如果有无限多个的公理，我们就无法把它们全写出来，
(9) Identity（恒等式）-----a mathematical expression giving the equality of two (often variable) quantities (trigonometric identities, Euler’s identity).
(10) Paradox（悖论）----a statement that can be shown, using a given set of axioms and de nitions, to be both true and false. Paradoxes are often used to show the inconsistencies in a awed theory (Russell’s paradox). The term paradox is often used informally to describe a surprising or counterintuitive result that follows from a given set of rules (Banach-Tarski paradox, Alabama paradox, Gabriel’s horn).
paradox
记忆技巧：para 旁边；外 + dox 教，观点 → 观点边有观点 → 自相矛盾
矛盾的人(或事物、情况);
似非而是的隽语; 悖论; 悖论修辞
'More haste, less speed' is a well-known paradox.
“欲速则不达”是人们熟知的似非而是的隽语。
|
222610
