1. Let m, n, p, q \in Z
If 0 < m < n and 0< p \leq q, then mp < nq
2. Propositions/axioms I can use that relate to inequalities
2.4 Let m,n,p \in Z. If m < n and n < p, then m < p
2.5 For each n \in N there exists an m \in N such that m > n
2.6 Let m,n \in Z. If m \leq n \leq m then...