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Math Help - Triangle inequality

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    Triangle inequality

    Let \epsilon be a fixed number in (0,1). Use a form of the triangle inequality to show that if a is a real number with |a-1|< \epsilon then |2-a|>1- \epsilon

    apparently i did this one completely wrong in the hw and now its on my exam review sheet
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by tn11631 View Post
    Let \epsilon be a fixed number in (0,1). Use a form of the triangle inequality to show that if a is a real number with |a-1|< \epsilon then |2-a|>1- \epsilon

    apparently i did this one completely wrong in the hw and now its on my exam review sheet
    |a-1|<\varepsilon\implies a-1<|a|-1<\varepsilon and thus 1-\varepsilon<1-(a-1)<|1-(a-1)|=|2-a|
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