(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm having an enormously hard time wrapping my head around the following definition, which is using some concepts that keep showing up in other definitions and theorems.

I'll state the definition and then i'll ask about the parts that i don't understand:

We say that [tex]limx_{n}=L[/tex] if for every positive number [itex]\epsilon[/itex] there exists a positive number N = N([itex]\epsilon[/itex]) such that [tex]\left | x_{n}-L \right |< \varepsilon [/tex] holds whenever n [itex]\geq[/itex] N.

2. Relevant equations

3. The attempt at a solution

Well the whole thing is just a big mess in my head, so the questions im able to formulate are:

What is this epsilon number? How is it related to N? Why is [tex]\left | x_{n}-L \right |< \varepsilon [/tex] when n [itex]\geq[/itex] N?

If these are irrelevant questions, can you please try to explain this definition from another viewpoint, maybe even graphically?

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# Homework Help: A confusing definition of limit of a sequence

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