For all a,b∈R we have the triangle inequality
∣a∣+∣b∣≥∣a+b∣ Setting a=x1−x2 and b=x2, we obtain
∣x1−x2∣+∣x2∣≥∣x1−x2+x2∣ That is
∣x1−x2∣≥∣x1∣−∣x2∣ It follows that there exist x1 and x2 for which inequality
∣x1−x2∣>∣x1∣−∣x2∣ holds. For example, if x1=2 and x2=-3 we have
∣2−(−3)∣>∣2∣−∣−3∣ or
∣5∣>∣2∣−∣3∣ that is
5>−1 Hence, the statement
∣x1−x2∣=∣x1∣−∣x2∣ is false.
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