Specialist Maths Introduction to Proof Lessons Unit 1 Topic 2 Year 11

This is a powerpoint introducing students to the notation and definitions required for proofs.

It covers the following dot points from the QLD 2025 Specialist Maths Unit 1 Syllabus:

•Define 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 ®.

•Express rational numbers as terminating or eventually recurring decimals and vice versa.

•Use the quantifiers ‘for all’ (∀) and ‘there exists’ (∃).

•Use the set notation symbol ‘is an element of’ (∈).

•Use implication, converse, equivalence, negation, contrapositive.

•Use the symbols for implication ( ⇒ ), equivalence ( ⟺ ), and equality ( = ).

•Use proof by contradiction.

•Prove irrationality by contradiction.

•Use examples and counterexamples.

•Prove results involving integers, e.g. proving that the product of two consecutive odd numbers is an odd number and 5n2+3n+6 ∀n∈Z is an even number.