I don't quite get the significance of the delta limit definition,(adsbygoogle = window.adsbygoogle || []).push({});

if n>N and |s_{n}−s|< ϵ , why does the limit converges

does this simply means that there exist a number ε such that if n is great enough it will be greater than s by ε?

But this doesn't make sense, because s is the value the sequence converges to, so s_{n}cannot be greater than s

what confuses me even more is that (-1)^{n}is a diverging sequence but

it satisfies |s_{n}-s| < ε for ε>1

Can someone clarify this concept, thank you

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# Confusion regarding delta definition of limit

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