1. The problem statement, all variables and given/known data I am just curious ? I have a feeling that completeness or the archimedean property relies on well ordering but I am not entirely sure. However, completeness funishes a supremum or infimum for any subset of R that is bounded above or below, respectively. 3. The attempt at a solution [tex]N \subset R[/tex] So if S is any non empty subset of N then, S is a subset of R. If S bounded below, it has a infima in R. By the archimedean principle we can find can an integer that is greater or equal to the infima which would be in S. Is there something that prevents me from doing this ? Like completeness relying on well ordering of N.