Theorem: meaning, definitions and examples

Used primarily in mathematics and logic. It is a statement or proposition that has been proven based on previously established statements and accepted logical principles.

• Pythagoras' theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
• The theorem was derived after extensive proofs were validated.

Used in logic, mathematics, and general discussion. It is a statement or assertion that expresses a judgement or opinion, often subject to proof or disproof.

• The proposition that all swans are white was disproven when black swans were discovered.
• He presented a business proposition to the investors.

Used in various fields including science, philosophy, and ethics. It refers to a foundational concept or rule that serves as the basis for a system of belief or behavior.

• The principle of conservation of energy states that energy cannot be created or destroyed, only transformed.
• She is a person of strong moral principles, always standing up for what she believes in.

Used in science, legal contexts, and social systems. In science, it is a statement based on repeated experimental observations that describes some aspect of the world. In legal and social contexts, it refers to a system of rules recognized as regulating the actions of members.

• Newton's first law of motion states that an object will remain at rest or in uniform motion unless acted upon by an external force.
• The law prohibits stealing and ensures that justice is served.

A theorem is a statement that has been proven to be true based on previously established statements, such as other theorems, axioms, and postulates. It is commonly used in mathematics.

• Pythagoras' theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
• Euclid's Theorem on the infinitude of prime numbers is a fundamental concept in number theory.

A principle is a fundamental truth or proposition that serves as the foundation for a system of belief, behavior, or reasoning. It is often used in broader contexts beyond mathematics, such as in science, ethics, and philosophy.

• The principle of conservation of energy states that energy cannot be created or destroyed, only transformed.
• One of the key principles of democratic societies is the right to freedom of speech.

An axiom is a statement that is accepted as true without proof. It forms the basis for other statements and reasoning in a theoretical framework, particularly in mathematics and logic.

• In Euclidean geometry, one of the axioms is that through any two points, there is exactly one straight line.
• The axiom of equality states that things which are equal to the same thing are also equal to one another.

A postulate is similar to an axiom but is typically used to describe basic assumptions within a specific theory, such as the starting points in geometry. It is something assumed without proof to be true within a given context.

• One of Euclid’s postulates is that a straight line segment can be drawn joining any two points.
• Einstein’s theory of relativity includes the postulate that the speed of light in a vacuum is constant.