Unformatted text preview: R a = { z : a z n + a 1 z n1 + ··· + a n1 z + a n = 0 } contains at most n elements. Thus, for n ﬁxed, [ a =( a ,...,a n ) ∈ Z n R a is a countable union of ﬁnite sets. Thus it is countable. The countability ntuples from a countable set was shown in class. Finall, the set of algebraic numbers is [ n ∈ N " [ a ∈ Z n R n # , which in tern is a countable union of countable sets and is thus countable. 1...
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 Spring '10
 MetCalfe
 Calculus, Sets, Natural number, Rational number, Countable set, J. Metcalfe

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