WJEC Mathematics for AS Level - Pure

1 Proof 16 Summary Check you know the following facts: Real numbers are those numbers that give a positive number when squared. Imaginary numbers when squared give a negative number (e.g. √ −1 when squared gives −1). Rational numbers can be expressed as fractions. Irrational numbers cannot be expressed as a fraction (e.g. π, √ 2, √ 3). To prove or disprove statements: • Use proof by exhaustion when it is possible to put all the values into a function/ expression to prove whether a statement is true or false. • Use proof by deduction if it is possible to use algebra to decide whether a particular statement is true or false. • Use disproof by counter-example if you can ϐind an example that is an exception to the statement or general rule.