Definition

1. Noun:
   • An idea accepted as a demonstrable truth: A statement or principle that has been proven to be true based on logic, reasoning, or previously established facts.
   • A proposition deducible from basic postulates: In mathematics and logic, a statement that can be derived from a set of axioms or postulates using accepted rules of inference.

Usage Examples

• Noun:
  • Pythagoras's theorem is fundamental to geometry.
  • The mathematician spent years proving the complex theorem.
  • We learned a new theorem in class today about prime numbers.

Advanced Usage

• "to prove a theorem": To demonstrate the truth of a theorem through a logical argument or mathematical proof.
  • She aims to prove the theorem using a novel approach.
• "by theorem": According to or as established by a theorem.
  • By theorem, the sum of the angles in a triangle is 180 degrees.

Variants and Related Words

• Theoretical (adj): Concerned with or involving the theory of a subject or area of study rather than its practical application.
  • His work is purely theoretical.
• Theorematic (adj): Of the nature of or relating to a theorem.
  • The theorematic proof was elegant.

Synonyms

• Principle: A fundamental truth or proposition that serves as the foundation for a system of belief or behavior or for a chain of reasoning.
• Law: A statement of fact, deduced from observation, to the effect that a particular natural or scientific phenomenon always occurs if certain conditions are present.
• Proposition: A statement or assertion that expresses a judgment or opinion.

Related Phrases

• Fundamental theorem: A theorem that serves as a foundation for a larger theory.
  • The fundamental theorem of calculus connects differentiation and integration.
• Existence theorem: A theorem that asserts the existence of an object with certain properties, without necessarily providing a method to find it.
  • The mathematician published an important existence theorem.

Idioms

(This word is highly technical and is not commonly used in idiomatic expressions. Its usage is primarily formal and academic.)

Noun

1. an idea accepted as a demonstrable truth
2. a proposition deducible from basic postulates