Archimedean group

An archimedean group is a way to think about numbers and how they relate to each other. Let's pretend you have a pile of candy and you want to share it with your friends. How do you decide how much candy each person gets?

One way to figure it out is by thinking about proportions. If you have twice as much candy as your friend, you can give them half of your pile and you'll both have the same amount. But what if you have a lot more candy than your friend? In that case, proportions won't work very well.

That's where archimedean groups come in. They help us compare numbers no matter how big they are. With an archimedean group, we can figure out if one number is bigger or smaller than another no matter how many times bigger or smaller it is.

For example, let's say you have 10 pieces of candy and your friend has 5 pieces. We can use an archimedean group to compare those two numbers. We can say that 10 is twice as big as 5, or we can say that 5 is half as big as 10.

But what if you have 100 pieces of candy? Or 1000? Or a million? With an archimedean group, it doesn't matter how big the numbers are. We can always compare them and figure out which one is bigger or smaller.

In summary, an archimedean group is a way to compare numbers no matter how big they are by using proportions and figuring out their relationships to each other.