Theorem

How it is used

You state, prove and apply a theorem. In textbooks and papers theorems are numbered (Theorem 3.2), often with a lemma before them and a corollary after them. A statement that is believed but not yet proved is a conjecture.

Example sentences

1. By the theorem we proved last week, the two angles must be equal.

2. State the theorem carefully before you apply it.

Common collocations

• prove a theorem
• state a theorem
• apply a theorem
• by the theorem
• fundamental theorem

Related terms

• proofA logical argument that shows, step by step from accepted facts, that a mathematical statement is always true.
• lemmaA smaller statement, proved on its own, that is used as a step towards proving a larger theorem.
• Pythagorean theoremThe rule that in a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².
• counterexampleA single example that shows a general statement is false; for the claim 'all prime numbers are odd', the number 2 is a counterexample.

More terms: Proofs and Mathematical Writing

• let x be
• proof by contradiction
• proof by induction
• QED
• without loss of generality
• it follows that