I learned about commutators from a guy on the front row who was really good at Rubik's cubes. Concrete examples relatable to your hobbies are great.
I also tried to pay for my lunch by commutating, but the lunch lady wouldn't have it.
- A pile without apples is a pile of apples. We call it the empty pile.
- The successor function is to add an apple to the pile. Apply the successor function to the pile of apples and you still have a pile of apples.
- A pile of apples is as large as itself
- If the left pile has as many apples as the right pile, then the right pile also has as many apples as the left pile
- If you have two piles of apples you can add them by checking if the second pile is empty. If it is empty you are done and the result is in the first pile. If not take an apple from the second pile and add it to the first pile. Then check again and repeat
And then you can teach him about the bijection between money and apples. After a little more set theory you can start constructing two piles of apples, one representing what you have one what you have to give away ...
The possibilities are endless.