Diagonalization Is Also Practically Useful: a Geometric Idea
نویسندگان
چکیده
Cantor’s diagonalization idea: reminder. Most mathematicians are familiar with diagonalization from Cantor’s proof that the set of all real numbers is not countable. Indeed, if it was countable, i.e., if we could enumerate all (decimal) real numbers d1d2 . . . di.f1 . . . fj . . . into a sequence d (k) 1 d (k) 2 . . . d (k) i .f (k) 1 . . . f (k) j . . ., k = 1, 2, . . ., then we would be able to design a new real number which is not in this sequence, by:
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