# Manipulating inequalities

by mjjoga
Tags: epsilon, inequalities, proof
 P: 14 so I have 1/(n-2). I have that n>max(epsilon+2,1). I need to get 1/(n-2) < epsilon. I know that 1/(n-2)<1/(epsilon+2-2)=1/epsilon. but 1/epsilon is not always less than epsilon. can you see any errors?
 P: 150 Your question is unclear.
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P: 21,258
 Quote by mjjoga so I have 1/(n-2). I have that n>max(epsilon+2,1). I need to get 1/(n-2) < epsilon. I know that 1/(n-2)<1/(epsilon+2-2)=1/epsilon. but 1/epsilon is not always less than epsilon. can you see any errors?
Epsilon is typically a small positive number that is much closer to 0 than it is to 1. Unless epsilon is negative, epsilon + 2 will be larger than 1.

1/(n - 2) < epsilon <==> n - 2 > 1/epsilon, making the reasonable assumptions that n > 2 and epsilon > 0.

If epsilon is small and positive, 1/epsilon is generally larger than epsilon.

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