Difference between revisions of "Real numbers"

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(oww, the pain, the pain. this is so bad. will try to clean it up. PAIN!)
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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.
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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]].

Revision as of 06:34, February 22, 2007

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 which is Ordered, Complete, and Archimedean. The reals can be constructed from the rationals by means of Dedekind cuts or Cauchy Sequences.

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