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

Assume the opposite of what we want to prove is true

Do math until a contradiction arises

Conclude the original statement must be true

Not all numbers are even

There exists at least one A that is not B

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

There exists a greatest integer $k$

$k + 1 > k$ contradicts $k$ being greatest

There exists odd $n^2$ such that $n$ is even

$2k + 1$

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

$a$ and $b$ both even, share common factor of $2$