axioms的音標是[?e?k???mz]，中文釋義為公理； 公理法。基本翻譯為“公理； 公理系統； 公理法； 公理法系統”。速記技巧可以考慮使用諧音記憶法，可以將公理的英文單詞“axioms”諧音理解為“埃克斯作業”，這樣方便記憶。

以下是關于公理（axioms）的一些英文詞源及其變化形式和相關單詞：

1. Axiom - 原意為“公理”，通常指被普遍接受的原則或真理，沒有證明或驗證的過程。它的變化形式包括其復數形式axioms，以及其過去式axiomized和過去分詞axiomized。相關單詞包括proof（證明）、validate（驗證）等。

2. Postulate - 原意為“假定”，通常指根據已知事實或經驗，提出作為論證基礎的前提或假設。它的變化形式包括其復數形式postulates和過去式postulated。相關單詞包括supposition（假定）、presuppose（預先假定）等。

3. Principle - 原意為“原理”、“原則”，通常指在某一領域或學科中，被廣泛接受并用于指導實踐的基本準則或規則。它的變化形式包括其復數形式principles和過去式principle-lize等。相關單詞包括fundamental（根本的）、tenet（信條）等。

4. Assumption - 原意為“假定”、“假設”，通常指根據某種理由或目的，做出某種推測或猜測。它的變化形式包括其復數形式assumptions和過去式assumed等。相關單詞包括 hypothesis（假設）、conjecture（猜測）等。

這些詞源都與科學、哲學、數學等領域中的基本原則和原理有關，通過這些詞源可以更好地理解公理的含義和重要性。同時，這些詞也反映了人類在探索真理和知識的過程中，不斷提出假設、驗證和證明的過程。

常用短語：

1. The law of the excluded middle

2. The principle of parsimony

3. The axiom of choice

4. The postulate of infinity

5. The postulate of the existence of irrational numbers

6. The axiom of infinity

7. The postulate of the existence of real numbers

雙語例句：

1. The axiom of choice helps us to solve difficult problems in analysis. (選擇公理有助于我們解決分析中的難題。)

2. The postulate of infinity is fundamental to modern mathematics. (無窮公理是現代數學的基礎。)

3. The law of the excluded middle is a useful tool for proving theorems in logic. (排中律是一個有用的工具，用于邏輯定理的證明。)

4. Parsimony is a guiding principle in scientific research, encouraging us to choose the simplest explanation for a phenomenon. (簡約原則是科學研究中的指導原則，它鼓勵我們為一種現象選擇最簡單的解釋。)

5. The postulate of irrational numbers is essential for understanding certain aspects of mathematical physics. (對于理解數學物理的某些方面，無理數公設是必不可少的。)

6. The axiom of infinity is fundamental to many branches of mathematics, allowing us to consider infinite sets and infinite sequences of numbers. (無窮公理對于數學許多分支是基礎，它使我們能夠考慮無限集合和無限數字序列。)

英文小作文：

The axiom of choice and its impact on mathematics

The axiom of choice plays a fundamental role in modern mathematics, allowing us to consider problems that would otherwise be intractable. It provides a framework for understanding certain complex mathematical concepts, such as measure and topology, and it has had a profound impact on the development of many branches of mathematics.

The axiom of choice states that it is always possible to select an element from an infinite set. This seemingly simple statement has profound implications for mathematical reasoning, as it allows us to consider infinite sets and sequences of numbers, which are not possible under more restrictive axioms. It also provides a solution to certain seemingly insoluble problems in analysis, allowing mathematicians to develop new theories and methods that have transformed the field.

The axiom of choice is not without controversy, however, as it has been criticized for being too general and lacking in precision. Nevertheless, its importance in mathematics cannot be denied, and it continues to be a fundamental tool for understanding and solving complex mathematical problems.