大家好，欢迎来到IT知识分享网。
定义（definition）、公理（axiom）、定理（theorem）、推论（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、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 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”).
(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).
(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).
免责声明：本站所有文章内容,图片，视频等均是来源于用户投稿和互联网及文摘转载整编而成，不代表本站观点，不承担相关法律责任。其著作权各归其原作者或其出版社所有。如发现本站有涉嫌抄袭侵权/违法违规的内容,侵犯到您的权益，请在线联系站长,一经查实,本站将立刻删除。 本文来自网络,若有侵权，请联系删除，如若转载，请注明出处：https://haidsoft.com/157220.html
