<Li> if a <b and c <d, then a + c <b + d </Li> <Li> if a <b and 0 <c, then ac <bc . </Li> <P> It follows that Z together with the above ordering is an ordered ring . </P> <P> The integers are the only nontrivial totally ordered abelian group whose positive elements are well - ordered . This is equivalent to the statement that any Noetherian valuation ring is either a field or a discrete valuation ring . </P>

What set of numbers does 5/6 belong to