Limit set

The limit set is like a special place that shows us where something happens again and again. Imagine you are riding a bike in a park and there is a big hill. Every time you ride down the hill, you go very fast and it feels exciting. You like it so much that you want to do it again and again.

Now, imagine you are a little ant and you are also riding down the hill on the bike. You cannot see the whole hill at once, but you can see the part where the exciting thing happens again and again. That exciting part is like the limit set for the ant.

In math, we use the limit set to see where a sequence or a function keeps doing the same thing over and over again. It is like finding a special place on a hill where something exciting happens every time we go there. We can mark that place and use it to understand how the sequence or function behaves.