1. Prove thata < b and c < 0 implies that b*c < a*c.
2. Prove that if 0 < a < b, then 0 < 1/b < 1/a
for this proof, it is assumed you know basic properties of numbers. in particular, that the product of two negative numbers is positive.
Assume and . Then . Therefore we must have , since this is the product of two negative numbers. Thus we have , as desired.