Is there anything like 'infinity'?

Suppose you encounter an algebraic term (n+1), where n is ANY number. Now, what is n? As said earlier, n could be any number. But the question that arises is that how do you know that (n+1) is also a number?  Maybe n is the highest number possible. 

We say things like - "...and this process goes on forever...." which means it goes on infinitely. But what does infinity mean here? That the process goes on forever. What is "forever" here? Forever in time, and time is measured in numbers, and they are precisely what the above argument applies to.