Number systems and rational forms
Sets and power sets
Primes and unique factorisation
Propositions and quantifiers
Direct and indirect proof
Mathematical induction
Identify the smallest standard real-number set containing an evaluated exact value, distinguishing natural numbers, integers, rationals and irrationals under the project convention Decide whether an expression denotes a real number, distinguishing division by zero, the indeterminate zero-over-zero form, principal even roots and non-real even roots Distinguish number-system containment and justify closure or counterexamples Convert between fractions, mixed numbers and decimals Construct an exact fraction by aligning and subtracting recurring decimal tails Distinguish an element statement from a subset statement and decide whether a finite set is contained in another stated set Form or recognise the union, intersection, difference and complement of finite or interval-defined sets relative to an explicitly stated universe Count all, proper and nonempty subsets of a finite set Primes, composites, factors and multiples Express a whole number as a product of prime factors in index form State unique prime factorisation and construct an argument for infinitely many primes Interpret propositions and quantified statements, and construct negations or counterexamples Construct direct, contrapositive and contradiction arguments with justified steps Construct induction proofs with a verified base, arbitrary-index hypothesis and justified next case