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The following contents are quoted from Prof. Dave Richeson's note.
The following contents are quoted from Prof. Dave Richeson's note.
Definition(定義)
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.
Theorem(定理)
A mathematical statement that is proved using rigorous mathematical reasoning. In a mathematical paper, the term theorem is often reserved for the most important results.
Lemma(補題)
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.
Corollary(系)
A result in which the (usually short) proof relies heavily on a given theorem.
Proposition(命題)
A proved and often interesting result, but generally less important than a theorem.
Axiom/Postulate(公理/公準)
A statement that is assumed to be true without proof. These are the basic building blocks from which all theorems are proved.
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