Jagged Numbers
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.
Additive & Multiplicative measures, Vectorial Metrics, Copula-Archimedean family flexibility, Extrapolation, Distribution, Statistical Inference, Additive Case, Ballistic Combinatorics, jagged numbers, Jagged Numbers, Change-point detection, Symmetry, square root, Kato's Nullity Theorem, Lemma, fully-jagged nested array, Additive & Multiplicative measures, Well-Ordered Sets, Random Variable, Smooth Milner Dynamics, Multivariate dependence, additively generated, Undo controls, Archimedean Copula, Non-Canonical Probability Theory, Meager Sets, Renyi Divergence, Perturbation Theory, Integer partition, Jagged, jagged natural, Inapplicability, Polynomial Arithmetic, Null Baire Categories, Erdos-Kac, Taylor expansion of the identity function, Kruskal's Tree Theorem, Distribution Functions, Finite Sets, Infinities, Jagged Natural Numbers Predicate, Edge Flipping, randomness, Parameterization, Renyi Entropy, Copula of Monotonicity, Copula-Archimedean family, Fishier-Random Walk, Copulas of interchangeability and independence, probability measure, Non-Canonical Probability Theory, Euclidean space, Multiplicative Structure, Copulas of monotonic transformations, Jagged-natural numbers, Free additive Number Theory, Indispensability, Polynomial Mapping Theorem, Diophantine Form Input, independent, Euclidean Dispersal, Euclidean Regularity, Multiplicative Case, isometric interpolating, Independent Causal Flow Networks, triangle inequality, Interpolation, Reference Frame Selection, condensation, Popper's Flop-Flop, Probability Distributions, weakly increasing, Taylor expansion of the identity function, copula, Mutation Distribution, Multivariate Real Analysis, Asymptotic Number Theory
Additive & Multiplicative measures, Vectorial Metrics, Copula-Archimedean family flexibility, Extrapolation, Distribution, Statistical Inference, Additive Case, Ballistic Combinatorics, jagged numbers, Jagged Numbers, Change-point detection, Symmetry, square root, Kato's Nullity Theorem, Lemma, fully-jagged nested array, Additive & Multiplicative measures, Well-Ordered Sets, Random Variable, Smooth Milner Dynamics, Multivariate dependence, additively generated, Undo controls, Archimedean Copula, Non-Canonical Probability Theory, Meager Sets, Renyi Divergence, Perturbation Theory, Integer partition, Jagged, jagged natural, Inapplicability, Polynomial Arithmetic, Null Baire Categories, Erdos-Kac, Taylor expansion of the identity function, Kruskal's Tree Theorem, Distribution Functions, Finite Sets, Infinities, Jagged Natural Numbers Predicate, Edge Flipping, randomness, Parameterization, Renyi Entropy, Copula of Monotonicity, Copula-Archimedean family, Fishier-Random Walk, Copulas of interchangeability and independence, probability measure, Non-Canonical Probability Theory, Euclidean space, Multiplicative Structure, Copulas of monotonic transformations, Jagged-natural numbers, Free additive Number Theory, Indispensability, Polynomial Mapping Theorem, Diophantine Form Input, independent, Euclidean Dispersal, Euclidean Regularity, Multiplicative Case, isometric interpolating, Independent Causal Flow Networks, triangle inequality, Interpolation, Reference Frame Selection, condensation, Popper's Flop-Flop, Probability Distributions, weakly increasing, Taylor expansion of the identity function, copula, Mutation Distribution, Multivariate Real Analysis, Asymptotic Number Theory
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