You probably know that you have fewer hands than there are letters in the English alphabet. You also probably know that there are fewer letters in the English alphabet than there are whole numbers. But are there `fewer' whole numbers than say, points on the number line between zero and one? Is it even well posed to ask whether one infinite collection of objects has `fewer' constituents than another infinite collection of objects? We will walk through how one makes sense of such questions. By the end, we will see that there really are different sizes of infinity (in fact, infinitely many). A great feature of this story is that, aside from remembering what numbers are, you don't need prior background in math, and the style of reasoning is pretty different from what you meet in a normal high school math class. So, people who think they don't like math are especially encouraged to give it a go.