Maths - Proof by Contradiction
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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”