Implementation of mathematics in set theory

Okay, so imagine you have a bunch of toys, like your stuffed animals or Legos. When you group them together based on some property, like all the animals with fur or all the red Legos, you're creating a set. Set theory is like a way of organizing those sets and figuring out how they relate to each other.

Now, when we want to use math to talk about sets, we need to use symbols and special rules. For example, we might use the symbol ∪ to mean "union," which is a fancy way of saying "combining two sets into one big set." So if we have a set of all the blue Legos and a set of all the red Legos, we could use the union symbol to show the set of all the blue and red Legos: {blue} ∪ {red} = {blue, red}.

Another important symbol in set theory is the ∈ symbol, which means "belongs to." It's used to show if an element (like a single Lego or stuffed animal) is in a set or not. So if we have a set of all the Legos and we want to show that one of them, say a blue one, is in the set, we could write: blue ∈ {all Legos}.

Some other important concepts in set theory include intersection (it's like the opposite of union, where you only get the elements that are in both sets), complement (which means all the elements that are not in a set), and cardinality (which is just a fancy way of saying how many elements are in a set).

Overall, set theory helps us use math to talk about groups of things and how they relate to each other. It might seem a little confusing at first, but just remember that the symbols and rules are just ways to make it easier to talk about different sets and the things that are in them.