Proof by Contradiction (AQA A-Level Mathematics): Flashcards

Assume the opposite of what we want to prove is true

Do some maths until a nonsensical statement arises

Conclude that the original statement must be true

Not all numbers are even / At least one number is odd

$\frac{a}{b}$ where $a$, $b$ are integers with no common factors

$2k$ where $k$ is an integer

$2k + 1$ where $k$ is an integer

Must state 'a contradiction'

$\sqrt{2} = \frac{a}{b}$ with no common factors, find contradiction

Both $a$ and $b$ are even, contradicting no common factors