Zermelo set theory

Zermelo Set Theory is a way that grown-ups think about a bunch of things called "sets." A "set" is just a group of things put together. Your toy box is a set of toys!

Now, imagine that there are different kinds of sets. Some sets have stuff in them that is not really important, like the set of all the things in your room. Other sets have things that are very important, like the set of all the prime numbers.

The idea of Zermelo Set Theory is to say that ALL sets are made up of smaller sets, which are called "elements." For example, the set of all the toys in your toy box is made up of smaller sets, like one set for the dolls and one set for the stuffed animals.

But here's where it gets tricky: what if we have sets that have sets inside them, like the set of all the sets that have only one element? This can be confusing because it sounds like we are talking about a set that contains itself!

To avoid this confusion, Zermelo Set Theory adds a rule that says a set cannot contain itself. This means that the set of all sets that have only one element cannot be a thing that exists.

Overall, Zermelo Set Theory helps grown-ups think about sets in a way that makes sense and doesn't allow for any weird loopholes.