n.公理

原形：axiom复数：axioms

The axiom of choice is a fundamental principle in set theory that states any collection of non-empty sets has a choice function.
选择公理是集合论中的一个基本原理，它指出任何非空集合的集合都存在一个选择函数。
Euclid's first axiom asserts that things which are equal to the same thing are also equal to one another.
欧几里得的第一公理断言，凡是等于同一样东西的其他东西也彼此相等。
The parallel postulate is an axiom in Euclidean geometry stating that through any point not on a given line, there is exactly one line parallel to the given line.
平行公设是欧几里得几何中的一个公理，它指出通过不在已知直线上任意一点，有且仅有一条直线与已知直线平行。
Axioms in mathematics are self-evident truths that form the foundation of logical deductions.
数学中的公理是指不言自明的真理，它们构成了逻辑推演的基础。
The Peano axioms define the properties of natural numbers, including the concept of zero and the process of counting.
皮亚诺公理定义了自然数的性质，包括零的概念和计数过程。
In physics, the principle of relativity is often treated as an axiom, asserting that the laws of physics are the same for all observers in uniform motion relative to one another.
在物理学中，相对性原理常被视为一个公理，它断言所有相对于彼此做匀速运动的观察者所观测到的物理定律都是相同的。
The reflexive property, an axiom in many mathematical systems, states that every element is equal to itself.
反身性属性是许多数学体系中的一个公理，它指出每一个元素都等于其自身。
Zermelo-Fraenkel set theory, with the axiom of choice, forms the basis for much of modern mathematics.
带有选择公理的策梅洛-弗兰克尔集合论构成了现代数学大部分内容的基础。
The Church-Turing thesis, while not strictly an axiom, is a foundational assumption in theoretical computer science about the nature of computable functions.
虽然丘奇-图灵论题严格来说不是一个公理，但它是在理论计算机科学中关于可计算函数本质的一个基础假设。
The well-ordering principle, an axiom equivalent to the axiom of choice, states that every non-empty set can be well-ordered.
良序原理是一个等价于选择公理的公理，它指出每一个非空集合都可以被良序排列。