Borel's theorem

Imagine you have a bunch of balls that you want to group into piles based on their color. Borel's theorem basically says that it's always possible to do this, even if you have an infinite number of balls or colors.

To understand it better, think of the color spectrum - red, orange, yellow, green, blue, purple, etc. - as a line. Borel's theorem says that you can always divide that line into different sections based on the colors you want to group together. For example, you could group red and orange together, yellow and green together, and blue and purple together.

This might seem obvious, but it's actually a really important idea in math. It helps us understand how to group things together in different ways, even if we have an endless amount of options to choose from. So, the next time you're sorting your toys by color, remember that you're using Borel's theorem without even realizing it!