Mathematical Proof

This module of Maths Extension 1 explores the concept of mathematical proof. A proof in mathematics uses formal logical reasoning to show that a statement is always true.

There are many different methods for proving mathematical statements, but this module focuses on one method called proof by induction.

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Proof by Induction

Proof by induction is a technique that allows us to prove a statement is true for an infinite number of cases — without checking every single case individually (which would be impossible).

Here’s the key idea:

1. Show the statement is true for a base case.
2. Prove that if the statement is true for one case, it is also true for the next case.

If we can do both steps, then the statement must be true for all cases that follow. This is a bit like a line of dominoes: If you can prove knocking over each domino will knock over the next one, then you know that pushing the first domino will knock down all of them, even if there is an infinite number of dominos.

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