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Equality is a fundamental concept in mathematics. Two numbers a and b are equal if they represent the same quantity or value. In this case, we write a = b. For example, if a = 3 and b = 3, then a = b.

The trichotomy property states that for any two real numbers, exactly one of the following is true: 1. a < b (a is less than b) 2. a = b (a is equal to b) 3. a > b (a is greater than b) This property is a fundamental axiom of the real number system, meaning it is accepted as true without the need for proof.

By the trichotomy property, for any two real numbers a and b, one and only one of these inequalities is true: a < b, a = b, or a > b. This means that: - If a < b, then a is less than b, and it is not equal to or greater than b. - If a = b, then a is equal to b, and it cannot be less than or greater than b. - If a > b, then a is greater than b, and it is neither less than nor equal to b. The trichotomy property guarantees that there are no other possibilities for the relationship between a and b. In conclusion, the trichotomy property shows that for any two numbers a and b, one and only one of the following is true: a is less than b, a is equal to b, or a is greater than b. This means that either a < b, a = b, or a > b.