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1,000,000,000,000,000; or cheese. It's cheese :).
By Misacek01: If you were looking for a number that would have no more numbers succeeding it, know that there is no such thing. The fact that a calculator will not display more digits has nothing to do with it.
There is a theorem, one of the very fundamentals of algebra. In some systems, it is even considered an axiom. It says that for every integer n there exists an integer (n+1). It follows from this that there are infinitely many numbers (not just integers, but this particular form of the theorem deals with nothing else so let's keep it simple). So, if you wrote digits from here to the Moon (or the other side of the galaxy, for that matter), there would still not only be a number greater than the one you have written, but an infinite amount of greater numbers.
The theorem I wrote about is known as the Axiom of Archimedes. Its original form is "For every real x there exists a real number n such that n > x." What I wrote follows from this and is more to our point. From this full form it may be seen that indeed not only integers, but the entire real line is infinite.