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.
对数学术语含义的精确而明确的描述。它通过给出一个词的所有性质，仅给出那些必须为真的性质，来表征该词的意义。
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.
用严格的数学推理证明的数学陈述。在数学论文中，术语定理通常是为最重要的结果而保留的。
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.
唯一目的是帮助证明定理的小结果。这是证明一个定理之路的踏脚石。极少情况下引理可以独立存在。
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”).
证明（通常是简短的）很大程度上依赖于一个给定定理的结果（我们经常说“这是定理A的一个推论”）。
Proposition（命题）
A proved and often interesting result, but generally less important than a theorem.
一个被证明的，通常很有趣的结果，但一般没有定理重要。
Conjecture（推测，猜想）
A statement that is unproved, but is believed to be true.
Claim（断言）
An assertion that is then proved. It is often used like an informal lemma.
未经证实但被认为是真实的陈述。
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.
没有证明，且假设为真的陈述。这些是证明所有定理的基本构造块。
Identity（恒等式）
A mathematical expression giving the equality of two (often variable) quantities.
两个（通常是可变的）量相等的数学表达式。
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 an awed theory. The term paradox is often used informally to describe a surprising or counterintuitive result that follows from a given set of rules.
一种使用一组给定的公理和定义，既正确又错误的陈述。悖论经常被用来显示敬畏理论中的矛盾。“悖论”一词通常被非正式地用来描述从一组给定规则得出的令人惊讶或违反直觉的结果。