Here we look at only the rules without going into their proofs. They are:
a < b, if and only, if b - a > 0.
If a < b and b < c, then a < c.
If a < b, then (a + c) < (b + c).
If a < b, then -a > -b.
If a < b and
x = 0, then ax = bx x < 0, then ax > bx x > 0, then ax < bx
x = 0, then ax = bx
x < 0, then ax > bx
x > 0, then ax < bx
6. If 0 < a < b, then 0 < 1/b < 1/a.