What Is a Limit?

Stand a step from the wall. Walk halfway there. Now walk halfway of what's left. And halfway again. You get closer and closer to the wall — infinitely close — but do you ever touch it? Each step halves the distance, so the wall is always half a step away. Yet somehow the distance shrinks to nothing. That 'infinitely close to, without arriving' is the heart of calculus. It's called a limit.