Question

Prove the Archimedean principle.

Answer 1

ill show you what I have and you can all find flaws:)

Answer 2

given real a,b with a>0 there is an integer n in N st b<na

if b<a set n = 1
if a<= b consider A = {k in N: ka<=b}
k is bounded by a/b
so E has finite supremum s in E
s is natural

set n = s+100, then n is in N
n>s
so n is not in E
so na>b