定义、公理、定理、推论、命题和引理的区别
定义（definition）、公理（axiom）、定理（theorem）、推论（四川黄龙corollary）、命题（proposition）、引理（lemma）之间的相互关系基本如下。
首先、定义和公理是任何理论的基础，定义解决了概念的范畴，公理使得理论能够被人的理性所接受。
其次、定理和命题就是在定义和公理的基础上通过理性的加工使得理论的再延伸，我认为它们的区别主要在于，定理的理论高度比命题高些，定理主要是描述各定义（范畴）间的逻辑关系，命题一般描述的是某种对应关系（非范畴性的）。而推论就是某一定理的附属品，是该定理的简单应用。
最后、附桂骨痛胶囊引理就是在证明某一定理时所必须用到的其它定理。而在一般情况下，就像前面所提到的定理的证明是依赖于定义和公理的。
WHAT IS THE DIFFERENCE BETWEEN A THEOREM(定理), A LEMMA（引理）,AND A COROLLARY（推论）?
PROF. DAVE RICHESON
(1) Definition（定义）------a preci and unambiguous description of the meaning of a mathematical term. It characterizes the meaning of a word by giving all the properties and only tho properties that must be true.
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(2) Theorem（定理）----a mathematical statement that is proved using rigorous mathemat-ical reasoning. In a mathematical paper, the term theorem is often rerved for the most important results.
说开头的成语(3) Lemma（引理）----a minor result who sole purpo 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").
(5) Proposition（命题）-----a proved and often interesting result, but generally less important than a theorem.
五谷丰收>线型结构(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 asrtion that is then proved. It is often ud like an informal lemma.
(8) Axiom/Postulate------（公理/假定）a statement that is assumed to be true without proof. The are the basic building blocks from which all theorems are proved (Eu-clid's ve postulates, Zermelo-Frankel axioms, Peano axioms).
烤红薯的营养价值中班亲子游戏(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 t of axioms and de nitions, to be both true and fal. Paradoxes are often ud to show the inconsistenci
es in a awed theory (Rusll's paradox). The term paradox is often ud informally to describe a surprising or counterintuitive result that follows from a given t of rules (Banach-Tarski paradox, Alabama paradox, Gabriel's horn).
