"Eventually" in mathematics means that something will happen after a certain amount of time or steps. It's like waiting for a friend to arrive. You know they will come, but you're just not sure when. In math, we use "eventually" to describe what will happen in the future when we go on counting or doing something.
For example, let's say we have a sequence of numbers, 1, 2, 3, 4, 5... and so on. If we want to say that each number in the sequence is bigger than the one before it, we can say that "eventually" every number in the sequence will be bigger than the previous one. This means that even though the first few numbers might not be bigger, as we keep counting, the trend will always be that the numbers are getting bigger.
So, "eventually" is like a clue – it helps us understand what will happen in the future, even if we're not sure when it will happen.