# Describe in simple terms the method of Proof by Induction

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Proof by Induction:

Suppose `n` is a number in the set of all natural numbers `NN = {1,2,3,...}`. To prove, using the method of induction, that a mathematical relation or formula is true for all `n` we first demonstrate that it is true for `n=1`. We then demonstrate that if it is true for any `n` this implies it is true for `n+1` (the next term in the series). This is the *inductive step*. Then, the relation must be true for all `n` because by the inductive step we have demonstrated that as well as it being true for `n=1` it is also true for `n=2` and hence for `n=3` and so on. This is a great saving on showing the result is true for each and every `n`, which in any case wouldn't be possible because `n`can be infinite.