WJEC Maths for A2 – 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 a fraction ( i.e. a b ) where a and b are integers with no common factors. Irrational numbers cannot be expressed as a fraction (e.g. π, √ 2, √ 3 ). Proof by contradiction Here we assume that a statement or what we want to prove is not true and then use maths techniques to show that the consequences of this are not possible. The consequences can contradict what we have just assumed to be true or something we know to be deϐinitely true (e.g. x 2 cannot be negative for real values of x ) or both. These are called contradictions to the original assumption.