Exponential field

An exponential field is like a big toy box full of numbers that can grow really fast if you keep playing with them. Imagine you have one toy car, and you want to make more toy cars: you take the car and make a copy of it. Now you have two. If you keep doing this, you can have four, then eight, then 16, and so on –and very soon you'll have too many toy cars to count!

An exponential field works just like that with numbers. Imagine you have a number, let's call it 2, and you want to make more numbers with it. So you multiply 2 by itself, and you get 4. Then you multiply 2 by 4, and you get 8. If you keep doing this, the numbers you get will grow very fast: 16, 32, 64, and so on.

But an exponential field is not just one number that grows like that. It's a whole bunch of numbers that you can use to do all kinds of calculations. And it's not just 2 that you can multiply by itself over and over again – you can use any number you like.

The special thing about an exponential field is that it has really clever rules that make all these calculations work really well. For example, no matter how many times you multiply a number in an exponential field by itself, you'll always end up with another number that's also in the exponential field.

So, imagine you have a great big toy box full of numbers that is an exponential field. You can pick a starting number, like many toy cars, and use it to get more and more numbers that go really fast like 2, and if you follow the rules there's no limit to how far you can go!