axiom

Also known as postulate

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'.

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 sections

Contents

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

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.