(adsbygoogle = window.adsbygoogle || []).push({}); 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 [itex]\epsilon[/itex] > 0 we have |an − L| < [itex]\epsilon[/itex] 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| < [itex]\epsilon[/itex] for every [itex]\epsilon[/itex] > 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 [itex]\in[/itex] 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.

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# Correct this improper definition of a limit

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