Discontinuous linear map

Ok kiddo, let's imagine we have two number lines, like long rulers that go on forever. A discontinuous linear map is like a way to move things from one ruler to the other, but not in a smooth way. It’s like we take each number on the first ruler, and we move it to a different number on the second ruler, but we don’t do it in a straight line. Instead, it’s like we jump around randomly from one spot to another.

For example, let's say we have a point on the first ruler that’s right in the middle, at number 5. Now let’s use the discontinuous linear map to move it to the second ruler. We might start by jumping it to number 2 on the second ruler, then jump it again to number 7, then 13, then 20, then 17, then back to 5 on the second ruler. We can keep jumping it like a rabbit until we get it to the other ruler.

So basically, a discontinuous linear map is a way to shuffle things around between number lines, but instead of doing it in a straight line, we jump around in a way that might seem random.