Meaning & Definition of word "Axiom"
to
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.