# Math Help - Triangle inequality

1. ## 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

2. Originally Posted by tn11631
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 $1-\varepsilon<1-(a-1)<|1-(a-1)|=|2-a|$