An information theorist studying data compression models determines that the efficiency factor of a specific algorithm is given by ϵ=log27\epsilon = \log_2 7ϵ=log27. A developer claims that this factor is a rational number and can be expressed exactly as a ratio of two integers pq\displaystyle \frac{p}{q}qp. Use the method of proof by contradiction to show that the developer's claim is incorrect.
132 exam-style questions on OCR (MEI) A Level Maths 1.1 Proof, covering 1.1.1 Structure of mathematical proof, 1.1.2 Disproof by counter example, 1.1.3 Proof by contradiction (A-level only), and 1.1 Proof. Each one has a worked solution and a mark scheme showing where the marks go.