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XE is the Cauchy-extension of X that can be identified with the set of limits of...

XE is the Cauchy-extension of X that can be identified with the set of limits of Cauchy sequences composed of elements of X, these limits need not be in X. Find (with proof) the Cauchy-extension of the metric space (Q, d) where d(x, y) = |x − y|. (You may wish to use the fact that any real number x has a decimal expansion. It may also be helpful to show that 10n > n for all n ∈ N.)

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