Existential theory of the reals

Okay kiddo, let's talk about something called the "existential theory of the reals." This is a fancy way of talking about how numbers (like 1, 2, 3, etc.) exist and work together.

You see, numbers are like friends that can interact with each other in different ways. Think of it like having a group of toys that you can use to play games. Sometimes you might add toys together to make a bigger group, or take them away to make a smaller group.

But sometimes, when you're playing with toys or numbers, you might find that there are certain things you can't do with them. For example, if you only have two toys, you can't make a group of three without adding more toys. In the same way, if you only have certain numbers, you might not be able to solve certain math problems without using other, more complicated numbers.

That's where the "existential theory of the reals" comes in. This theory helps us understand which numbers we can use to solve different kinds of math problems, and which ones we can't. It's like having a set of rules that tells us what we can and can't do with our toys.

Overall, the "existential theory of the reals" is just a way of understanding how numbers work together, and what we can do with them to solve different kinds of math problems.