# Maths - Proof by Contradiction

> Source: https://ollybritton.com/notes/a-level/maths/topics/proof-by-contradiction/ · Updated: 2021-06-06 · Tags: school, maths, proof

## See Also
- [Maths - Proof Roots of Primes are Irrational](https://ollybritton.com/notes/a-level/maths/topics/proof-roots-are-irrational/)
- [Maths - Proof](https://ollybritton.com/notes/a-level/maths/topics/proof/)

## Flashcards
##### How can you prove a statement is FALSE by contradiction??
Find a counterexample.

##### How can you prove a statement is TRUE by contradiction??
* Negate the statement and assume it's false.
* Prove this leads to a contradiction.

##### What would be the negated statement for "if $n^2$ is even, $n$ must be even"??
"there exists an odd number $n$ such that $n^2$ is even"

##### What would be the negated statement for "there are infinitely prime numbers"??
"there is a finite number of prime numbers"

---
Olly Britton — https://ollybritton.com. Machine-readable index: https://ollybritton.com/llms.txt