Steinitz's theorem
Steinitz's theorem is a big math idea that talks about shapes – but not just any old shapes, shapes that are made up of points. Each point represents a different value, just like how the numbers 1, 2, and 3 are all different.
Now, imagine you have a bunch of these points. You can move them around and make different shapes. But there’s one important rule you have to follow: none of the points can be exactly the same. It’s like if you’ve already used a number, you can’t use it again – that would be cheating!
Steinitz's theorem says that you can take any shape made up of these points and you can “stretch” and “squish” it as much as you want, and as long as you follow the one important rule, it will still be the same shape. In grown-up terms, this is called an "isomorphism".
So basically, Steinitz's theorem says that all shapes made up of points are actually the same in a way as long as you don't cheat with the rule. Cool, huh?
Now, imagine you have a bunch of these points. You can move them around and make different shapes. But there’s one important rule you have to follow: none of the points can be exactly the same. It’s like if you’ve already used a number, you can’t use it again – that would be cheating!
Steinitz's theorem says that you can take any shape made up of these points and you can “stretch” and “squish” it as much as you want, and as long as you follow the one important rule, it will still be the same shape. In grown-up terms, this is called an "isomorphism".
So basically, Steinitz's theorem says that all shapes made up of points are actually the same in a way as long as you don't cheat with the rule. Cool, huh?