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On Feb. 20, I followed your suggestion of having an example of generating an irrational number by using Cantor's 1874 method. This follows the example of generating an irrational number by using Cantor's diagonal method. — [[User:RJGray|RJGray]] ([[User talk:RJGray|talk]]) 01:19, 3 March 2010 (UTC)
== Restrict polynomials to irreducible ones in proof of countability of algebraic numbers? ==
As far as I understood Cantor's 1874 article, he considers in his proof of countability of algebraic numbers only [[irreducible polynomial]]s (p.258: "''und die Gleichung (1.) irreducibel denken''" = "''and consider equation (1.) to be irreducible''"). These are sufficient to get all algebraic numbers, and each of them corresponds to at most one algebraic number, viz. its root (if in ℝ). In this setting it is more clear what it means to "''order the real roots of polynomials of the same height by numeric order''" (cited from [[Cantor's first uncountability proof#The proofs]]). Maybe the article should also restrict polynomials to irreducible ones - ?
[[User:Jochen Burghardt|Jochen Burghardt]] ([[User talk:Jochen Burghardt|talk]]) 15:10, 13 December 2013 (UTC)
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