axiom
Sign in to savethumb|The parallel postulate which states if the sum of the interior angles of two lines is less than 180°, the two straight lines meet on that side. The postulate is correct on a flat plane in [[Euclidean geometry but breaks on curved geometries such as spheres.]] An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.
AI overview
An axiom is a statement that is accepted as true without needing to be proven, serving as a starting point for reasoning and building other ideas upon it. Axioms matter because they form the foundation of logical systems—for example, in geometry, different axioms about how lines behave lead to different types of geometry, some that work on flat surfaces and others that work on curved ones.
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Article
23 sectionsContents
- Etymology
- Historical development
- Early Greeks
- Modern development
- Other sciences
- Mathematical logic
- Logical axioms
- Examples
- Propositional logic
- First-order logic
- Non-logical axioms
- Examples
- Arithmetic
- Euclidean geometry
- Real analysis
- <span id="role">Role in mathematical logic</span>
- Deductive systems and completeness
- Further discussion
- See also
- Notes
- References
- Further reading
- External links
thumb|The parallel postulate which states if the sum of the interior angles of two lines is less than 180°, the two straight lines meet on that side. The postulate is correct on a flat plane in [[Euclidean geometry but breaks on curved geometries such as spheres.]] An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.
The precise definition varies across fields of study. In classical philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. In modern logic, an axiom is a premise or starting point for reasoning.