Unreal Numbers
8 days ago
- #set theory
- #mathematics
- #real numbers
- The article discusses the construction of natural numbers from first principles using Peano arithmetic and set theory.
- It explores the extension of natural numbers to integers and rational numbers, defining operations like addition and multiplication.
- The concept of computable numbers is introduced, highlighting that their cardinality is the same as natural numbers.
- Real numbers are defined using Dedekind cuts, showing their uncountable infinity and the existence of uncomputable numbers.
- The article concludes with philosophical musings on the nature of reality and the limits of computability.