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# total order of real numbers

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Real numbers can be compared (on the real line) with the order relation. For we define

If such a comparison allows equality, the symbols and are used.

Positive real numbers are denoted by

and, analogously, negative real numbers by . Moreover, .

Real numbers are complete with respect to the order relation. This means that for every bounded set of real numbers there exists a least upper bound (supremum) and a greatest lower bound (infimum) in .

(Authors: Höllig/Kimmerle/Abele)