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Cauchy sequences of rationals can be used to model the reals.

Has anyone actually tried though to develop a theory of real analysis explicitly in this model?

Some definitions seem like they would be straightforward to convert into this model, but I am not sure about others.

I guess we probably wouldn't gain anything, but it would be interesting to see.

Does someone have a reference maybe?

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    It is not clear whether one could could obtain such sequences in a canonical way. Maybe via continued fractions.2013-11-07

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