Millie is attempting to use proof by contradiction to show that the result of multiplying an irrational number by a non-zero rational number is always an irrational number - AQA - A-Level Maths Mechanics - Question 4 - 2021 - Paper 1

To start Millie's proof by contradiction, she should assume that there exists a non-zero rational number and an irrational number whose product is rational. This assumption is crucial as it sets the stage for her to explore the implications and eventually lead to a contradiction, demonstrating that the original statement (the product must always be irrational) is indeed valid.