Cantor's Non-Equinumerosity Theorems, Inductively
Logic
2025-10-20 v1
Abstract
We apply an inductive argument to three theorems of Cantor on (1) the uncountability of infinite binary sequences, (2) the uncountability of real numbers, and (3) the non-equinumerosity of sets with their powersets. This technique proves the powerset theorem by assuming the Axiom of Choice.
Cite
@article{arxiv.2510.15321,
title = {Cantor's Non-Equinumerosity Theorems, Inductively},
author = {Saeed Salehi},
journal= {arXiv preprint arXiv:2510.15321},
year = {2025}
}
Comments
7 pages