QED

How it is used

Read letter by letter: 'Q-E-D'. In modern textbooks and papers it is often replaced by a small square (□ or ∎) at the end of the proof. Students sometimes also say 'QED' as a joke when they win an argument.

Example sentences

1. Therefore n² is even, which is what we wanted to show. QED.

2. Our lecturer writes QED at the end of every proof instead of the little square.

Common collocations

• Q.E.D.
• end of proof
• tombstone symbol
• write QED

Related terms

• proofA logical argument that shows, step by step from accepted facts, that a mathematical statement is always true.
• theoremAn important mathematical statement that has been proved to be true, such as the Pythagorean theorem.
• lemmaA smaller statement, proved on its own, that is used as a step towards proving a larger theorem.
• it follows thatA linking phrase used in proofs and solutions to show that the next statement is a logical result of what has just been shown.

More terms: Proofs and Mathematical Writing

• let x be
• counterexample
• proof by contradiction
• proof by induction
• without loss of generality