Learning objectives
Write simple deductive proofs, numerical and algebraic, working from one side of an identity to the other and using the symbols for equality (=) and identity (≡) correctly
Use algebraic representations such as 2n + 1 for an odd number to prove general statements about integers and about their sums, differences and products
(HL) Prove a statement by mathematical induction, setting out the base case, the inductive hypothesis, the inductive step and the conclusion, for results involving series, divisibility, inequalities, derivatives and complex numbers
(HL) Prove a statement by contradiction by assuming its negation and deriving an impossibility, for example that √2 is irrational or that there are infinitely many primes
(HL) Disprove a conjecture by finding a counterexample, and explain why a single counterexample is enough to show that a statement is not always true
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