What is the difference between two statements of $\varepsilon-N$ definition? Here is a homework question, TRUE/FALSE:
$$\lim_{n\to\infty}a_n=a\Longleftrightarrow$$


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*$\forall\varepsilon>0,\ \exists N\in\mathbb{Z^+},\ \text{whenever}\ n>N\Rightarrow|a_n-a|<\varepsilon$. Answer: TRUE

*$\exists N\in\mathbb{Z^+},\forall\varepsilon>0,\ \ \text{whenever}\ n>N\Rightarrow|a_n-a|<\varepsilon$. Answer: FALSE 
I am confused that what is difference between 1 & 2 (or say why No.2 is wrong)? 
Thanks!

The second statement says, in effect, that there comes a point beyond which all the terms of the sequence are exactly equal to $a$.
