The axiom of equality states that things equal to the same thing are equal.
等式公理指出，等于同一事物的事物是相等的。
In mathematics, an axiom is a statement accepted as true without proof.
在数学中，公理是被接受为真而无需证明的陈述。
Euclidean geometry is based on a set of fundamental axioms.
欧几里得几何基于一组基本公理。
An axiom is often used as a starting point for further reasoning.
公理常被用作进一步推理的起点。
The axiom of choice is a controversial mathematical principle.
选择公理是一个有争议的数学原理。
Every logical system is built upon certain foundational axioms.
每个逻辑系统都是建立在某些基础公理之上的。
In science, an axiom is a premise so evident as to be accepted.
在科学中，公理是显而易见的前提，因而被接受。
The self-evident nature of an axiom makes it universally accepted.
公理的自明性使其被普遍接受。
Philosophers debate whether an axiom can truly be unquestionable.
哲学家争论公理是否真的可以毫无疑问。
Logical deductions rely heavily on the validity of initial axioms.
逻辑推理严重依赖于初始公理的有效性。
axiom schema 公理模式
axiom of extensionality 外延公理
axiom of infinity 无限公理
axiom of power set 幂集公理
axiom of regularity 正则公理
axiom of pairing 配对公理
复数: axioms;
