Number theory
Why do numbers go on forever?
Hi Amanda, That's a very good question. Here's a sort of mathematical game that shows THAT numbers go on forever. Suppose someone came up to you and said that 117 was the largest number. What would you say? You'd probably say, "That's not true! There are lots of numbers bigger than 117. For instance, 118, 119, and 135." But what if they said, "OK, then how about a googol? That's the number that is written with a 1 then 100 zeros after it (like one thousand is a 1 with 3 zeros after it). Do you know a number bigger than that?" At first, that seems like a hard question, but even if we don't know the special NAME for any number bigger than a googol, we know that there is one, because no matter what number you name, I know that there's a larger number. Suppose I told you that I had a machine count the number of grains of sand in the Sahara Desert and that was the largest number possible. You could say, "That can't be the largest number, since if I go to the Gobi Desert and pick up one grain of sand and bring it to the Sahara, we've described a number that is 1 more than the number you said was the biggest possible!" That trick will ALWAYS work. For instance, we know that a googol is the not the biggest number, since a googol plus 1 is even bigger. But that's not the biggest number, either, because you could add 1 to that, and then 1 to that, and so on. Since you could keep adding 1 forever, we'll never get to the largest number (you can always add 1 more). So, numbers go on forever because you can always add 1 more!