axiom
gb/ˈæksiəm/ us/ˈæksiəm/
C1
Anh
Các nghĩa
0 nghĩa
Danh từ
formal
C1
rule
1
basic principle accepted as true
a basic idea most people accept as true
Mẫu sử dụng:
the axiom that [clause]; an axiom of [field]
Lỗi thường gặp:
Learners may overuse axiom for any opinion; it usually implies something generally accepted or treated as unquestionable.
Từ đồng nghĩa
principle (Broader and more common; may not be treated as self-evident.)
|
maxim (Often a moral or practical saying.)
|
truism (Emphasizes that it is obviously true, sometimes to the point of being unhelpful.)
Từ trái nghĩa
paradox (A statement that seems contradictory or defies common sense.)
|
fallacy (A mistaken belief or faulty reasoning presented as true.)
Cụm từ đi kèm
a well-known axiom
|a common axiom
|an old axiom
|a basic axiom
|a central axiom
|a guiding axiom
|an axiom of philosophy
|an axiom of economics
|challenge an axiom
|accept an axiom
Chủ đề
education
|thinking
|communication
Ví dụ
- In journalism, it’s almost an axiom that speed and accuracy are in tension.
- She questioned the axiom that success always requires long hours.
- The book treats individual freedom as a political axiom.
Ví dụ cho người học
- It is an axiom that practice helps you improve.
- He disagrees with that axiom.
Danh từ
technical
C2
rule
2
assumed starting statement in math
a rule in math that you accept without proof
Mẫu sử dụng:
an axiom of [system]; take [statement] as an axiom
Lỗi thường gặp:
Do not confuse an axiom (assumed) with a theorem (proved within the system).
Từ đồng nghĩa
postulate (Common in geometry and formal contexts; very close in meaning.)
|
assumption (More general; may be temporary or not foundational.)
Từ trái nghĩa
theorem (A statement proved from axioms and definitions.)
Cụm từ đi kèm
a set of axioms
|axioms and theorems
|an axiom system
|an axiom schema
|derive from axioms
|prove from axioms
|independent of the axioms
|consistent with the axioms
|add an axiom
|choose axioms
Chủ đề
mathematics
|logic
|education
Ví dụ
- Euclidean geometry is built on a small number of axioms.
- If you change one axiom, you can get a different kind of geometry.
- The proof relies only on the axioms given at the start.
Ví dụ cho người học
- In math, an axiom is accepted without proof.
Ngữ pháp
Dạng từ điển
axiom
IPA
GB/ˈæksiəm/
US/ˈæksiəm/
Âm tiết và trọng âm
ax - iom (2 âm tiết)
Stress on 1st syllable (ax)
Các dạng từ
Noun
- Base: axiom
- Plural: axioms
Họ từ
Forms
axioms
noun
Core family
axiomatic
adjective C1
Advanced or less common
axiomatically
adverb
axiomatize
verb
axiomatization
noun
Cách diễn đạt
axiom of choice
1/ˈæksiəm əv t͡ʃˈɔɪs/
fixed phrase
technical
set theory selection principle
a famous rule used in set theory
Ví dụ
- Some proofs in analysis rely on the axiom of choice.
- The axiom of choice is independent of certain other axioms of set theory.
euclid's axioms
1/ˈuklɪdz ˈæksiəmz/
fixed phrase
technical
classical geometry starting rules
the basic rules used in Euclidean geometry
Ví dụ
- Non-Euclidean geometries arise when you alter one of Euclid's axioms.
- The lecture compared Euclid's axioms with modern axiom systems.
it is an axiom that
1/ˈɪt ˈɪz ən ˈæksiəm ðˈæt/
fixed phrase
formal
introduce an accepted principle
used to say something is widely accepted as true
Ví dụ
- It is an axiom that data quality matters more than data quantity.
- For many trainers, it is an axiom that rest is part of progress.
peano axioms
1/pˈinoʊ ˈæksiəmz/
fixed phrase
technical
foundation of natural numbers
a set of rules that define natural numbers
Ví dụ
- The course introduced the natural numbers via the Peano axioms.
- From the Peano axioms, you can formalize proofs about addition and multiplication.