The problem follows
"Using the Completeness Axiom for R, prove the Archimedian property of the real numbers : for any x in R, there is an integer n>0 such that n>x "
I tried to prove it in a reductio ad absurdumd. But I can't....
(I tried in this way) : for a fixed x in R, assume n<=x for all interger n. since left side diverges to infinity so, x cannot be fixed. therefore the assumption is not the case, there exists n s.t n>x.
I think my proof has some problems.. and I don't know how I can prove it using the Completeness Axiom.