Definitions
- Used in mathematics and logic to refer to a self-evident or universally accepted statement. - Describing a fundamental principle or truth that serves as a basis for reasoning or argument. - Referring to a statement that is accepted without proof and used as a starting point for further deductions or conclusions.
- Used in mathematics and geometry to refer to an assumption or proposition that is taken as true without proof. - Describing a hypothesis or assumption made at the beginning of a scientific investigation. - Referring to a statement that is accepted as true based on observation or experience, but may not be universally accepted.
List of Similarities
- 1Both are used in mathematics and logic.
- 2Both refer to statements or propositions that are accepted as true.
- 3Both serve as starting points for further reasoning or deductions.
- 4Both are used to establish the foundation of a theory or argument.
What is the difference?
- 1Proof: Axioms are accepted without proof and are considered self-evident or universally accepted. Postulates may be based on observation, experience, or assumptions, but they may not be universally accepted and may require further proof.
- 2Uniqueness: Axioms are generally unique and specific to a particular system or field of study. Postulates can vary between different theories or investigations and may not be universally applicable.
- 3Usage: Axioms are commonly used in mathematics and logic. Postulates are used in mathematics, geometry, and scientific investigations.
- 4Acceptance: Axioms are widely accepted and form the basis of a theory or argument. Postulates may be subject to debate or revision based on new evidence or discoveries.
Remember this!
Axiom and postulate are both terms used in mathematics, logic, and scientific investigations. They both refer to statements or propositions that are accepted as true and serve as starting points for further reasoning. However, the difference lies in their origin, proof, uniqueness, usage, and acceptance. Axioms are universally accepted and self-evident, while postulates may be based on observation, experience, or assumptions and may not be universally accepted.
