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oww, the pain, the pain. this is so bad. will try to clean it up. PAIN!
Real numbers are comprised of all positive and negative values and zero, including rational, irrational and infinite values. Real numbers exclude the imaginary square roots of all negative numbers.
Real numbers can be thought of as numbers which can be represented by some infinite decimal representation. More rigorously, the real numbers are the unique [[Field (mathematics)|field]] which is [[Ordered]], [[Complete (mathematics)|Complete]], and [[Archimedean]]. The reals can be constructed from the rationals by means of [[Dedekind cuts]] or [[Cauchy Sequences]].