Proof

The second year adds the most powerful method of all: assume the opposite, and show that it leads to something impossible. Proof by deduction, exhaustion and counter-example from Year 1 are all still examinable, and often appear inside other topics.

• An Overview — the four methods of proof, how to choose between them, and the common mistakes

The content statements

• Proof by Contradiction — negating a statement, the irrationality of √2, the infinitude of primes, and number-theory results

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Each page has step-by-step notes, several worked examples, a quick-reference grid and ten practice questions with fully worked solutions.