2004/03/15 by W. Mueckenheim, Mueckenheim, W.
Computer Science · Mathematics · #03E25 #03E35 #Computability, Logic, AI Algorithms #FOS: Mathematics #General Mathematics (math.GM) #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.math/0403238
openalex publication_date 2004/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notions of potential infinity (understood as expressing a direction) and actual infinity (expressing a quantity) are investigated. It is shown that the notion of actual infinity is inconsistent, because the set of all (finite) natural numbers which it is ascribed to, cannot contain an actually infinite number of elements. Further the basic inequality of transfinite set theory aleph0 < 2aleph0 is found invalid, and, consequently, the set of real numbers is proven denumerable by enumerating it.