# Correct this improper definition of a limit

by Easy_as_Pi
Tags: correct, definition, improper, limit
 P: 31 1. The problem statement, all variables and given/known data Eddy wrote on his midterm exam that the definition of the limit is the following: The sequence {an} converges to the real number L if there exists an N ∈ Natural numbers so that for every $\epsilon$ > 0 we have |an − L| < $\epsilon$ for all n > N. Show Eddy why he is wrong by demonstrating that if this were the definition of the limit then it would not be true that lim n→∞ 1/n = 0. (Hint: What does it mean if |a − b| < $\epsilon$ for every $\epsilon$ > 0?) 2. Relevant equations |a-b| <ε means that ||a|-|b|| < ε from the reverse triangle inequality 3. The attempt at a solution I know it has to do with the fact that the actual definition of a limit has "for every ε > 0, there exists an N $\in$ Natural numbers S.T. ...." so, Eddy reversed that part of the definition. I just haven't been able to quite see the difference of the two. A little push in the right direction would be greatly appreciated. I like figuring these out on my own, so no full on answers, please.