Disjoint union

Have you ever played with different sets of toys? For example, you have a box of cars and another box of dolls. Each box contains different types of toys and they don't mix with each other. That's what disjoint union is like.

In math, we use sets (like boxes of toys) to represent a bunch of things that have something in common. For example, we can use a set to represent all the animals in a zoo. But sometimes, we want to combine sets to make a new set. That's where disjoint union comes in.

Disjoint union is like making a new set by combining two or more sets, but without any overlap. Think of it as putting all the toys in one big pile, but separating them by type. So all the cars go in one pile and all the dolls go in another pile. They don't mix together because they are in different piles.

In math, we show disjoint union using a special symbol that looks like a plus sign with a dot on top. So if we want to combine the set of cars and the set of dolls, we write it like this:

cars ⊔ dolls

When we do this, we get a new set that contains all the cars and all the dolls, but they don't have any common elements. This means that if we try to find something that is both a car and a doll, we won't find anything.

So that's what disjoint union is all about. It's a way of combining sets without any overlap, just like separating your toys into different piles.