Subsequential limit

Hey kiddo, have you ever played a game where you try to catch a ball that is bouncing all around the place?

Now, imagine you have an infinite number of balls that drop from the sky, each one landing at a different spot. Some of the balls land close to each other, and others are very far apart.

A subsequential limit is like finding the spot where the most balls consistently land as they bounce around.

Let's say one of the balls lands in a spot, and then another ball bounces and lands close to that spot, and then even more balls keep landing around that same spot. Eventually, you notice that this spot is getting crowded with balls all the time! That spot is called a subsequential limit because it shows where the balls tend to land consistently.

Similarly, in math, when we have an infinite number of numbers, we can look at them bouncing around and notice where they tend to cluster consistently. This cluster is called a subsequential limit.