system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5 What Calculus is, and what it's used for.

I've heard of it, and the most I understand is that it's advanced maths, insanely hard, and some of the stuff I learned at GCSE (Age 14) can be done much faster with it. Unfortunately, past age 15 (I'm now 22) I didn't learn any more maths - I did French, Spanish and Politics A Levels, and a degree in the same. I'm not asking to learn it, just wondering what the deal with it is.
gpt
Imagine someone is walking, but according to very strange rules. On their first step they travel one meter. Every step after that is then half the length of the previous step. That means the second step is 1/2 a meter, the third step is 1/4 a meter, then 1/8, 1/16, 1/32, etc.

It's not too hard to figure out how far the person has traveled after a certain number of steps. After 1 step, the person has traveled 1 meter. After two steps 1 1/2, three steps 1 3/4, four steps 1 7/8, and so on. With a little patience, you could figure out the distance for the 158273877629th step.

But what would happen if that person were to take an infinite number of steps? How far would he go? Would he go an infinite distance, or would he actually stop somewhere? This is the kind of thing calculus helps you figure out.

There is a *limit* to how far this strange walking man can travel if he adheres to these rules. In this case that limit is 2 meters. No matter how many steps he takes, he will never travel past 2 meters. Any finite number of steps he takes (i.e. any number like 5, 10 or 837626, no matter how big) he will be short of 2 meters by some amount, but once he takes an infinite number of steps he will "arrive" at 2 meters.

Normal math can't handle things like infinity very well. In many cases, where to get your answer you would have to add an infinite number of things, or divide by zero, calculus lets you get around this in clever ways, and it's all based on the idea of *limits*.

Let's call the number of steps the man takes "n", and the distance he has traveled "x". As the number of steps the man takes (n) increases (as n approaches infinity) the distance he has traveled gets closer to 2 (x approaches 2). If we put those mathy terms together we get, "As n approaches infinity, x approaches 2". This means the *limit* of x is 2. As long as n is finite, x is less than 2. If n becomes infinite, then x becomes 2.