Describe the properties of inequalities, Mathematics

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Describe the Properties of Inequalities ?

Postulate
In comparing two quantities, say a and b, there are exactly three possibilities.
(1) a is less than b. (a < b) (2) a is equal to b. (a = b) (3) a is greater than b. (a > b)

Notice:
1. a < b and b > a are equivalent expressions.
2. All the above statements are true if we replace the symbol "<" with ">".
3. If a < b and c > d, then no conclusion can be stated regarding how the values of a + c and b + d compare.

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