axiom

axiom — 名詞

1. a short saying or rule that most people treat as obviously true and use as a sta

1.名詞C1
釋義

格言；通則

大家普遍相信為真的道理或說法

a short saying or rule that most people treat as obviously true and use as a starting point when thinking or arguing about something.

例句

Grandma Rosa lived by the old axiom that honesty saves you trouble in the long run.

蘿莎奶奶一向奉行那句老格言：誠實長遠來看能讓你少惹麻煩。

axiom that + clause stating the principle

Chef Lin reminded her students of the kitchen axiom that fresh ingredients matter more than fancy tools.

林主廚提醒學生那條廚房裡的通則：新鮮食材比花俏的工具更重要。

an axiom that + clause stating a field principle

同義詞
  • maxim

    more about rules for personal behaviour

  • adage

    an old, traditional saying passed down over time

  • truism

    often slightly negative — so obvious it adds little

  • principle

    broader; a basic rule guiding action or thought

反義詞
  • fallacy

    a belief widely thought correct but actually wrong

文法句型

axiom that + clause

axiom of + noun

用法筆記

Subject is usually an idea or saying about life, work, or behaviour. Distinguish from sense 2: this sense names a popular belief, while sense 2 names a formal starting rule in maths or science.

常見錯誤

❌I told my friend an axiom about the weather yesterday.
✅I shared an old saying about the weather with my friend.
💡'axiom' refers to a widely accepted general truth, not a casual remark or daily comment.

2. in maths, logic, or science, a basic rule that you agree to treat as true withou

2.名詞C2
釋義

公理；公設

數學或邏輯中不需證明、直接接受的起點規則

in maths, logic, or science, a basic rule that you agree to treat as true without proof, then use to build other rules and results from.

例句

Euclid built his geometry on five axioms about points, lines, and angles.

歐幾里得以五條關於點、線、角的公理作為他幾何學的基礎。

build [theory] on + axioms

Our teacher showed how every theorem in the chapter follows from three simple axioms.

老師示範這一章每條定理如何由三條簡單的公理推導而來。

follow from + axioms

同義詞
  • postulate

    near-identical in maths; chosen as a starting assumption

  • premise

    any starting statement in an argument, not only formal systems

  • first principle

    the most basic idea a field rests on, less technical

反義詞
  • theorem

    a result proved from axioms, not assumed

文法句型

axiom of + field

from this axiom + clause

用法筆記

Almost always plural in real use ('the axioms of ...'). Distinguish from sense 1: here the rule is taken as true by formal agreement inside a system, not because most people believe it. Often paired with 'theorem', 'proof', or 'postulate'.

常見錯誤

❌The teacher proved the axiom in front of the class.
✅The teacher proved a theorem using the axiom in front of the class.
💡axioms are accepted without proof; what gets proved from them is a theorem.