Meaning & Definition of word "Axiom"
Axiom
/ˈak.si.əm/
noun:
- 1. A statement or proposition that is regarded as being accepted, self-evidently true, and which serves as a starting point for further reasoning or arguments.
- Example: In mathematics, an axiom serves as the foundational truth upon which theorems are built.
- 2. A universally accepted principle or rule.
- Example: One common axiom of economics is that people act in their own self-interest.
- 3. An accepted or established rule in a particular field.
- Example: The axiom that 'all men are created equal' is a cornerstone of democratic societies.
- 4. A self-evident truth that requires no proof.
- Example: The axiom of identity states that each thing is identical to itself.
Etymology
●From Greek 'axiōma', meaning 'that which is deemed worthy or fit.'
Common Phrases and Expressions
axiom of choice:
A principle in set theory that asserts the ability to select an element from each set in a collection of nonempty sets.
self-evident axiom:
An axiom that does not require proof because its truth is obvious.
Related Words
theorem:
A statement that has been proven based on previously established statements.
hypothesis:
A proposition made as a basis for reasoning without any assumption of its truth.
postulate:
A statement that is assumed to be true in order to prove further statements.