The properties of inequality
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Description
Table 5. The properties of inequality. Here a, b and c stand for arbitrary numbers in the rational or real number systems.
| Exactly one of the following is true: a < b, a = b, a > b. |
| If a > b and b > c then a > c. |
| If a > b, then b < a. |
| If a > b, then –a < –b. |
| If a > b, then a ± c > b ± c. |
| If a > b and c > 0, then a x c > b x c. |
| If a > b and c < 0, then a × c < b x c. |
| If a > b and c > 0, then a ¸c > b ¸ c. |
| If a > b and c < 0, then a ¸c < b ¸ c. |
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