Nowhere dense set

Okay, so let's imagine you have a big box. Inside the box, there are all kinds of things, like toys and books and clothes. Now, let's say you have a special toy - let's call it a block - that you really like.

But here's the thing: the box is really full, and there's no way you can fit the block in with all the other things without moving some of them around. In fact, no matter where you try to put the block, you always end up moving some of the other things out of the way.

This is kind of like a nowhere dense set. A set is just a bunch of things, like the things in the box. A nowhere dense set is a special kind of set that doesn't have any place for other things to fit in without moving some of the things that are already there.

So, imagine a set that's like the box, and imagine you have a special point in that set - let's call it a dot - that you really like. No matter where you try to put that dot in the set, there's no way to do it without moving some of the other points around.

That's kind of what a nowhere dense set is - it's a set that's so full that you can't add any new things to it without moving some of the things that are already there.