Nested intervals

Okay kiddo, let me tell you a story about nested intervals. Imagine you have a bunch of sticks of different sizes. Each stick has two ends, one on the left and one on the right.

Now, let's say you take a stick and put it on top of another stick. The ends of the top stick will either be to the left or to the right of the ends of the bottom stick.

If the top stick is shorter than the bottom stick, then its ends will be somewhere inside the ends of the bottom stick. We call these ends "nested" because they are inside.

Now, imagine you take another stick and put it on top of the second one you just used. The same thing will happen: its ends will be nested inside the ends of the second stick.

This is where things get interesting. Even if you keep putting more and more sticks on top of each other, their ends will still be nested inside the ends of the bottom stick.

This means that if you keep doing this forever, you will end up with an infinite number of sticks with their ends nested inside the ends of the very first stick you put down.

Scientists and mathematicians are really interested in this because it helps them understand things that are infinite, or never-ending. They use it to solve all sorts of problems in math and science.

So there you have it, nested intervals are a bunch of sticks (or numbers, or anything really) that are stacked on top of each other, each one with its ends nested inside the ends of the one below it. And it can keep going on and on forever. Cool, huh?