The nature of proof

Specialist Mathematics · Unit 1 — Combinatorics, proof, vectors and matrices · Introduction to proof

Learning objectives (7)

LO-1Define and use set notation of number systems, including integers (ℤ), positive integers (ℤ+), negative integers (ℤ−), rational numbers (ℚ), irrational numbers (ℚ′), and real numbers (ℝ).LO-2Use examples and counterexamples.LO-3Use implication, converse, equivalence, negation, contrapositive.LO-4Use proof by contradiction.LO-5Use the quantifiers ‘for all’ (∀) and ‘there exists’ (∃).LO-6Use the set notation symbol ‘is an element of’ (∈).LO-7Use the symbols for implication ( ⇒), equivalence ( ⟺), and equality ( =).

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