Borel set

Imagine you have a big box full of different toys. Some of the toys are red, some are blue, and some are green. Now, let's say you want to make a special group of toys that you can only play with on special occasions, like your birthday or Christmas.

In order to make this special group of toys, you need to pick out certain toys from the big box. You can't just pick any toy, it has to meet certain criteria. You might decide to only include toys that are red or blue, and that are a certain size.

This process of selecting certain toys based on specific criteria is kind of like how we create Borel sets. A Borel set is a special group of numbers, and we create it by selecting certain numbers from a larger group of numbers. Just like how we selected certain toys from the big box based on color and size, we select certain numbers based on specific criteria.

So, what kind of criteria do we use to create a Borel set? Well, it depends on what we're trying to do. But generally speaking, we might select numbers based on things like their size, their location on a graph, or their relationship to other numbers.

Once we've selected these numbers, we put them into a special group called a Borel set. This set is kind of like our special box of toys that we only play with on special occasions. And just like we can do special things with our special box of toys, we can do special things with our Borel set of numbers, like use them to solve math problems or make predictions about the real world.