Cantor's Non-Equinumerosity Theorems, Inductively
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912654140899328 |
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| author | Salehi, Saeed |
| author_facet | Salehi, Saeed |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cantor's Non-Equinumerosity Theorems, Inductively Salehi, Saeed Logic 03E10, 03E25 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. |
| title | Cantor's Non-Equinumerosity Theorems, Inductively |
| topic | Logic 03E10, 03E25 |
| url | https://arxiv.org/abs/2510.15321 |