Suppose f : Q ? Q, f(x n ) is Cauchy for every Cauchy sequence x n . Show that the extension f : R ?

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Suppose f : Q → Q, f(xn) is Cauchy for every Cauchy sequence xn. Show that the extension f : R → R by f([xn]) = [f(xn)] is well-defined, i.e. if for Cauchy sequences xn ∼C yn, f(xn) ∼ f(yn)

 

 

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