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2. Definition and properties of the body of real numbers
2.1 Insufficiency of the body of rational numbers
The body of rational numbers is an example of a totally ordered body. However, this remains insufficient for the purposes of Analysis, due to the negative results we are now presenting:
(a) a positive rational number does not necessarily have a square root (and more generally a root n ) in ;
(b) a non-empty major (respectively minor) part of
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Definition and properties of the body of real numbers
Appendix: Principle of the construction of the body of real numbers
