QED
High School
Definition
An abbreviation of the latin phrase quod erat demonstrandum ("that which was to be demonstrated"). It signifies that we have come to the end of a proof. This is especially useful when it's not obvious that a proof has been completed.
Worked examples
Prove: \(\sqrt{2}\) is irrational. [proof steps...] Therefore no such integers exist. QED
QED appears after the final conclusion to signal the proof is complete.
Show \(a^2 - b^2 = (a-b)(a+b)\). Expand right side: \(a^2 + ab - ab - b^2 = a^2 - b^2\). QED
Even in short proofs, QED marks the finish line clearly.
Common mistakes
- Writing QED in the middle of a proof when only one case is done → Use QED only after all cases and steps are complete QED means the entire proof is finished, not just a partial result.
- Placing QED before the final conclusion statement → Write the conclusion, then QED on the same or next line QED comes after you state what was demonstrated, not before.
Where you'll use it next
You'll write QED at the end of geometric proofs, algebraic proofs, induction arguments, and formal reasoning in higher mathematics courses and logic.
Found in 1 StudyPug lesson
Deductive Reasoning: The Foundation of Logical Thinking
KindergartenKindergartenGeometry
Discover the power of deductive reasoning to draw specific conclusions from general premises. Enhance your problem-solving skills, critical thinking, and decision-making abilities through our comprehensive introduction.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026