A student named Elena makes the claim that there is a finite set of prime numbers P={p1,p2,p3,…,pk}P = \{p_1, p_2, p_3, \dots, p_k\}P={p1,p2,p3,…,pk} where pk p_k\,pk is the largest prime. Use the method of proof by contradiction to show that Elena's claim is incorrect, and thus prove that there are infinitely many prime numbers.
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.
