1. The problem statement, all variables and given/known data prove that if a; b; c are natural numbers and if a < b and b < c, then a < c. Some axioms we are allowed to use is if a<b then there exists a natural number e such that a+e=b. 3. The attempt at a solution If a<b then there is a natural number x such that a+x=b, if b<c then there exists a natural number y such that b+y=c, Now since b= a+x then a+x+y=c and since x+y is a another natural number, call it z then a+z=c which implies a<c. Is this the correct way to go about it.