A theoretical chemist determines that a specific bond length LLL is an irrational number. In a molecular model, they define an effective length EEE by scaling LLL by a known non-zero rational factor κ\kappaκ, such that E=κLE = \kappa LE=κL.
Prove by contradiction that the effective length EEE must be an irrational number.
107 exam-style questions on Edexcel A Level Maths 1.1 Proof by Contradiction. Each one has a worked solution and a mark scheme showing where the marks go.