The four main types of proof you need to be familiar with in A-level mathematics:
- proof by deduction
- proof by exhaustion
- proof by counter-example
- proof by contradiction
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100 greatest theorems of all time - http://pirate.shu.edu/~kahlnath/Top100.html
More videos on proof:
Proof by exhaustion example - https://youtu.be/4Gw9OzgC7Oc
Proof by contradiction example - https://youtu.be/jkhKPySIHgY
Proof by deduction example - https://youtu.be/ECPytIkS5YI