Paradoxes of set theory

A paradox in set theory is when something that you would think would be true turns out to be false. For example, think about a group of people. You would think that if you collected all the people in the group together and wrote down their names on a piece of paper (or in a set), that the list of names would be the same no matter who did it. But that's not always the case! Sometimes when you put the names in a set, it turns out that the list looks different depending on who made it. This is called a paradox because it seems like the answer should be the same no matter who is writing it down, but it's not.