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Full Idea
Cantor taught us to regard the totality of natural numbers, which was formerly thought to be infinite, as really finite after all.
Gist of Idea
Cantor presented the totality of natural numbers as finite, not infinite
Source
report of George Cantor (works [1880]) by John Mayberry - What Required for Foundation for Maths? p.414-2
Book Ref
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.414
A Reaction
I presume this is because they are (by definition) countable.
Related Idea
Idea 17797 Cantor extended the finite (rather than 'taming the infinite') [Mayberry]
| 17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
| 17423 | The essence of natural numbers must reflect all the functions they perform [Sicha] |
| 9965 | There couldn't just be one number, such as 17 [Jubien] |
| 13676 | Only higher-order languages can specify that 0,1,2,... are all the natural numbers that there are [Shapiro] |
| 8923 | Numbers are identified by their main properties and relations, involving the successor function [MacBride] |
| 17877 | The number series is primitive, not the result of some set theoretic axioms [Almog] |