【英语】axiom的例句
时间: 2024-11-07 14:55:51
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当谈论数学或逻辑学时，“axiom”指的是一个被接受为真实的基本原理或命题。以下是关于“axiom”的例句及其中文解释：
1. The axiom of choice states that from any collection of non-empty sets, it is possible to choose a function that assigns to each set an element of that set.
- 选择公理表明，对于任何非空集合的集合，都可以选择一个函数，该函数将每个集合映射到该集合的一个元素。
2. In Euclidean geometry, the parallel postulate is an axiom that states that for any given line and point not on the line, there is exactly one line through the point that does not intersect the given line.
- 在欧几里得几何中，平行公设是一个公理，它指出对于给定的一条直线和不在直线上的一点，通过该点有且只有一条不与给定直线相交的直线。
3. One of the axioms of arithmetic is that any number added to zero remains unchanged.
- 算术的一个公理是任何数加零保持不变。
4. A fundamental axiom in set theory is the axiom of extensionality, which states that two sets are equal if they have the same elements.
- 集合论中的一个基本公理是外延公理，它指出如果两个集合具有相同的元素，则它们相等。
5. The axiom of regularity in set theory ensures that every non-empty set has an element disjoint from it.
- 集合论中的正则性公理确保每个非空集合都有一个与之不相交的元素。
6. According to Gödel's completeness theorem, any consistent set of axioms for arithmetic has a model.
- 根据哥德尔的完全性定理，任何关于算术的一致公理集合都有一个模型。
7. The axiom of symmetry in economics posits that if person A prefers choice X over choice Y, then person B should prefer choice Y over choice X.
- 经济学中的对称公理假设如果个体A更喜欢选择X而不是选择Y，则个体B应该更喜欢选择Y而不是选择X。
8. A basic axiom of logic is the law of non-contradiction, which states that a statement cannot be both true and false at the same time and in the same sense.
- 逻辑学的一个基本公理是矛盾律，它指出一个命题不能在同一时间和同一意义上既为真又为假。
9. The axiom of choice has profound implications for the foundations of mathematics, influencing the development of various mathematical theories.
- 选择公理对数学基础具有深远的影响，影响了各种数学理论的发展。
10. Euclid's axioms formed the basis of classical geometry, providing a systematic framework for reasoning about shapes and spaces.
- 欧几里得的公设构成了古典几何学的基础，为推理形状和空间提供了系统的框架。
11. The axiom of continuity in physics suggests that physical quantities change continuously over time and space.
- 物理学中的连续性公理表明物理量随时间和空间连续变化。
12. One of the axioms of quantum mechanics is that the state of a system is represented by a vector in a Hilbert space.
- 量子力学的一个公理是系统的状态由希尔伯特空间中的一个向量表示。
13. The axioms of probability theory provide a mathematical foundation for reasoning about uncertainty and randomness.
- 概率论的公理为推理不确定性和随机性提供了数学基础。
14. Kant's categorical imperative operates on the axiom that moral actions should be universalizable.
- 康德的范畴命题是基于道德行为应该是普遍化的公理运作的。
15. The axiom of fallibility reminds us that no human knowledge is infallible; all beliefs should be open to critical examination.
- 易犯错公理提醒我们，没有人类知识是绝对无误的；所有信念都应该接受批判性审查。
这些例句展示了“axiom”在不同学科领域中的应用，包括数学、物理学、逻辑学以及伦理学等，每个例句后面都附有中文解释以便理解其含义和背景。