Normed division algebra

Okay kiddo, a normed division algebra is kind of like a toy box with some rules. Let me explain.

Imagine you have a toy box with some special toys in it. You can add, subtract, multiply and divide these toys, but there are some rules you have to follow.

First, these toys are all special because they have a special number attached to them. This number is called a norm and it tells you how big the toy is. Just like how you can say a big toy is bigger than a small toy, the norm tells you if one toy is bigger than another.

Second, you can only divide some of these toys with other toys. For example, you can divide a toy car with a toy bus, but you can't divide a toy car with a toy elephant.

Finally, you can't break any of the rules. If you try to divide a toy with another toy that you're not supposed to, like a toy car with a toy elephant, then you won't get a good answer.

So a normed division algebra is like a toy box with toys that have special numbers attached to them, you can only divide some toys with other toys, and you have to follow the rules or you won't get a good answer.