Let a,b,c any element of R
a. if a>b and b>c, then a>c
Proof
given a>b and b>c
will be proven a>c
proof
a>b --> a-b Є P .................... Definition
b>c --> b-c Є P .................... Definition
(a-b)+(b-c)Є P .............. Definition
<--> (a+(-b))+(b+(-c))Є P ......... Definition
<--> a+((-b)+b)+(-c) Є P ......... Assosiatif
<--> a+0+(-c)Є P ......... Invers
<--> a+(-c)Є P ......... Identitas
<--> a - c Є P ......... Definition
<--> a > c ......... Definition
so, Proven that a>c and b>c then a>c
