Definition and properties of the body of real numbers
Body of real numbers

The body $\mathbb{Q}$ 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 $\mathbb{Q}$ ;

(b) a non-empty major (respectively minor) part of