This is from anaylsis This is the details for the problem Th

This is from anaylsis:

This is the details for the problem:

This is the actual problem:

Suppose that GCR is a non-empty set. We say that G is a group of R if, given any two numbers E G, y E G, we have y E G and y E G

p= inf {x in G:x>0}

If p>0 then p is the smallest positive number in G

Suppose if possible p is not smallest member in G then there exists a positive member say c in G smaller than p

c<p ,which contradicts that p is

inf of {x inG : x>0} hence p is the smallest positive member of G

G={np:n in Z}

Let x in G then x belongs to R,as G is subgroup of R

If x>0 then inf G= p

And hence you can write G={p,2p,3p,..}

If x<0 ,G={-p,-2p,-3p,....}

G={np,p in Z}