Distance set

A distance set is when you have a group of points, and you want to find how far apart each point is from every other point. It's like if you have a bunch of toys, and you want to measure how far apart they are all from each other.

Imagine you have three toys: a teddy bear, a toy car, and a doll. You can measure the distance from the teddy bear to the toy car, from the teddy bear to the doll, and from the toy car to the doll. Those are all the different distances you can measure with those three toys.

Now imagine you have a lot more toys, like 10 or 20 or even 100. Finding all those different distances can be hard, especially if you don't have a lot of time or if you want to do it really quickly.

But scientists and mathematicians have figured out ways to make it easier. They use something called a matrix, which is like a big square with numbers in it. Each number tells you how far apart two toys are from each other. So if you had a matrix for those three toys, it might look like this:

| 0 | 5 | 3 |
|---|---|---|
| 5 | 0 | 2 |
| 3 | 2 | 0 |

That tells you that the teddy bear is 0 units away from itself (which makes sense, because it's not moving anywhere!), 5 units away from the toy car, 3 units away from the doll, and so on.

So now, instead of measuring all those different distances by hand, you can just look at the matrix and see how far apart every toy is from every other toy. And that's what a distance set is!