Theorem 18. If a < b , then a + c < b + c
Theorem 19. If a < b and c > 0 , then ac < bc .
Theorem 20. If a ≠ 0 , the a^2 > 0
Theorem 21. 1 > 0
Theorem 22. If a < b and c < 0 , then ac > bc
Theorem 23. If a < b ,then -a > -b . In particular , if a < 0 , then -a > 0
Theorem 24. If ab > 0 , then both a and b are positive or both are negative.
Theorem 25. If a < c and b < d , then a + b < c + d .
Theorem 26. Two different numbers cannot be least upper bounds for the same
set .
Theorem 27. Every nonempty set S that is bounded below has a greatest lower
bound ; that is ,there is a real number L s. t. inf S = L.
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