Complex sentence: The foundation of real analysis is the construction of the real numbers from the rational numbers, usually either by Dedekind-Macnielle Completion, Dedekind cuts, or by completion of Cauchy sequences.
Split into simpler sentences: The foundation of real analysis is the construction of the real numbers from the rational numbers. This is usually carried out by Dedekind-Macneille completion, Dedekind cuts, or by completion of Cauchy sequences.