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.
Practise AQA A Level Maths 1.4 A: Proof with exam-style questions for A Level Maths. 107 questions covering 1.4.1 Structure and methods of proof, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
