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An axiom is a starting rule that people treat as true, so they do not keep proving it every time. In maths and logic, axioms are the first stones: you agree they hold, then you build the rest on top of them. A geometry book may call something like “through two points there is one straight line” an axiom.
An axiom is a starting rule that people treat as trueaxiom是一條人們當成真的起始規則，so they do not keep proving it every time所以不用每次都重新證明它。In maths and logic在數學和邏輯裡，axioms are the first stonesaxiom是第一批基石：you agree they hold你先同意它們成立，then you build the rest on top of them然後在上面建構其他東西。A geometry book may call something like "through two points there is one straight line" an axiom幾何課本可能會把像「through two points there is one straight line過兩點只有一條直線」這樣的話稱作axiom。
In everyday talk, people also use axiom for a principle a group takes as given — “It’s an axiom of this kitchen that you clean as you go” — though actually that everyday use is looser. It means “we do not argue this any more,” not “this was laid down as a formal first truth.” The word feels educated and a little formal.
In everyday talk在日常對話裡，people also use axiom for a principle a group takes as given人們也會用axiom來指一群人視為理所當然的原則——"It's an axiom of this kitchen that you clean as you go"像「It's an axiom of this kitchen that you clean as you go在這個廚房，邊做邊清是條axiom」——though actually不過其實 that everyday use is looser這種日常用法比較鬆散。It means "we do not argue this any more,"它的意思是「這件事我們不再爭論了」，not "this was laid down as a formal first truth."而不是「這是被正式訂下的第一條真理」。The word feels educated and a little formal這個字聽起來有教養，也有點正式。
You will meet it in school maths, in philosophy, and in writing that wants to sound sure.
You will meet it in school maths, in philosophy, and in writing that wants to sound sure你會在學校數學、哲學，還有想聽起來很篤定的文章裡遇到它。
It is not a for opinion. An opinion is what you think; an axiom is what a system, or a group, refuses to keep arguing about.
It is not a synonym for opinion它不是opinion的同義詞。An opinion is what you think對某件事的opinion是你自己怎麼想；an axiom is what a system, or a group, refuses to keep arguing about而axiom則是一個系統或一群人拒絕再繼續爭論的東西。
組成From French axiome, from Latin axiōma, from Greek axiōma: “that which is thought fit,” a principle a pupil is expected to know already. That comes from a verb meaning “to think worthy,” and from áxios, “worthy,” literally “weighing as much as,” from a verb “to weigh.”
同家族的字
- axiomaticthe adjective: true in the way an axiom is true, so you do not need to prove it
原始詞典資料3 筆記錄
以下是外部詞典記錄的用法，原文照列，我們還沒有寫成教學內容。上面的說明才是我們自己寫的；有些用法可能上面已經講過了。
axiomnoun/ˈak.sɪ.əm/
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human-sciencesphilosophysciencesA seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
- Near-synonyms: given, facticity
- Neither can I reconcile this opinion of yours, with your argument brought from reaſon; if the axiom there laid down by you be true, it follows that, when matter began to exiſt in the divine mind, either matter became of the nature of the divine mind, i.e. active and intelligent, or elſe the divine mind became of the nature of matter, i.e. inert and unintelligent: this is a hard dilemma; have we not reaſon to ſuſpect that axiom?
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human-scienceslogicmathematicsA fundamental assumption that serves as a basis for deduction of theorems; a postulate (sometimes distinguished from postulates as being universally applicable, whereas postulates are particular to a certain science or context).
- Holonym: formal system
- Near-synonyms: given, facticity
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An established principle in some artistic practice or science that is universally received.
- The axioms of political economy cannot be considered absolute truths.
- But these innovating Medicaſters have introduced a Practice not only very precarious, but in many Reſpects extremely dangerous, and quite devoid of any one of the Qualities which conſtitute a good Remedy, viz. to cure the Patient, as the Axiom has it, cito, tuto, & jucunde, i.e. ſpeedily, ſafely, and pleaſantly.
資料來源：英文維基詞典 English Wiktionary（CC BY-SA 4.0）。 原文照列，未經改寫。