There are some truly huge numbers out there, and no matter what number you name, there are ALWAYS bigger ones.
One of the most well-known is googol (say Google). It's a 1 followed by 100 zeros, and looks like this:
10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.
Almost as well known is the googolplex. This is a 1 followed by a googol zeros. To demonstrate how incomprehensibly huge that is, if you wrote a zero on every atom in the universe, you would still not have enough zeros.
There are larger numbers than even this, though. It's actually possible to construct names for ANY number, based on a system of naming things which uses a lot of Latin. Many numbers higher than a googol have been written this way, but I'm not sure about higher than a googolplex.
Probably the highest finite number used in a mathematical proof was Graham's number. To give you an idea of how huge it was, think about 3+3+3. Not very impressive, I know, but we came up with a shorter way of writing that sort of thing. 3x3. Now, think about 3x3x3. We write that shorter now too, as 3 3. Amazingly, we can carry this forward further... we could also have 3 3^3 in there. Which some people write as 33. Now, 3x3 is 9. 3 3 is 27. And 33 is 7,625,597,484,987. This operation, called 'tetration' is clearly makes things get big fast. But why stop there?
Tetration is generally considered the fourth operation of the series. None of the others have names, they're just referred to by their symbols. Arrows with numbers next to them. Tetration can be written this way too - 33 is also seen as 3| 4|3. The next level is written like this: 3| 5|3. It's big enough that calculators no longer care, and will give you an error message. But this is not the Graham's Number. Graham's Number is 3| 64|3. I don't know how to put that in perspective, and I'm not even sure the number of digits is known, so I'll let you deal with that reality on your own, and keep in mind the sudden gap between 3 3 and 33.
More abstract are numbers technically even larger than this one, but they're infinite. Technically, they're still numbers, but even Graham's Number does end. We'll never know exactly how, but we know it does. Amazingly, modern mathematics has even given us numbers greater than infinity itself. I'm not going to explain them here, but if you really want the info, Wikipedia has a pretty good article on them. Search for 'Aleph numbers'.
