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Theorem and Proof: Absolute Value Function
THEOREM 1 Let a and b be real numbers. (i) a = a. (ii) ab = a · b. (iii) If b ≠ 0, a/b = a / b PROOF We use the equation x = (i) a===a (ii) ab == = = a · b. (iii) The proof is similar to (ii). Warning The equation a + b = a + b is false in general. For example, 2 + (3) = 1, while 2 + (3) = 5.


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