Jagged Numbers

In this article, we present the concept of jagged numbers, a novel way of representing real numbers using jagged natural numbers, which are a combination of vectors and differential forms. Using jagged numbers, we define a bijection between the natural numbers and the unit square, providing a new method for enumerating real numbers. We then use this bijection to prove two main theorems: the first stating that the only rational curve on the unit square is the identity, and the second showing the uniqueness of the copula isometric to the unit square. Our results have implications in mathematical logic, set theory, and geometric measure theory. Potential applications include computer science, statistics, and cryptography. Overall, we demonstrate the value of developing new mathematical structures for its own sake, as it may yield results that are not only aesthetically appealing but also useful in practical applications.