My nephew asked for some help with some mathematics. I thought that it would be a good thing to think about while I had breakfast. So I have the following explanation about proof by induction.

If Pete has toast and jam for breakfast today, then it means that he will definitely have toast and jam for breakfast tomorrow.

This will mean that he will always have toast and jam for breakfast, but only when he has had it at least once. If he always has porridge for breakfast then he will never have toast and jam.

It is not good enough just to show that Pete had toast and jam for breakfast two days in a row. You have to prove that if he has toast and jam for breakfast one day he will definitely have toast and jam for breakfast the next day.

I will post a couple of worked examples later – give my nephew the chance to try them first.