Hi! I need some help with this question:

**(a)**
Statement reads: For every $\displaystyle \epsilon$ there exists a point in the sequence $\displaystyle N \in N$ after which all terms lie between the lines $\displaystyle y= L-\epsilon$ and $\displaystyle y= L+ \epsilon$.

Now if we interchange the quantifiers it reads: There exists $\displaystyle N \in N $for every $\displaystyle \epsilon > 0$ such that for every point greater than or equal to N, all terms are between the lines $\displaystyle y= L-\epsilon$ and $\displaystyle y= L+ \epsilon$.

(sigh), it's the same thing! What's the difference if we interchange the two quantifiers? And how do we go about proving it? I tried everything, even drew a diagram. But man it’s hard...

So any help here is appreciated.