The Meaning of Infinity
W. Mueckenheim
Abstract
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.
Create a lesson
Related papers
A Note on the Measure of Vector and Pythagorean Theorem
Yu. V. Brezhnev
On Weighted Convex Graphs
Angshuman R. Goswami
On characterizations, Decompositions, and Stability of Convex Sequences
Angshuman R. Goswami
New Laplace convolution integrals involving exponential, error, and parabolic cylinder functions with applications in heat transfer and linear viscoelasticity
González Santander, Juan Luis
Resolution of Singularities in Positive Characteristic: Frobenius-Hasse Towers and Exceptional-History Descent
Chenxiao Tian
Information Geometry (IG) Lives at Edge or Boundary of SMG (statistically meaningful geometry): - the First Edge Theorem and Applications
Bing Cheng, Yi-Shuai Niu, Howell Tong et al.