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From what I've seen, I don't really understand how the definition means much of anything (visual examples included.) All it seems to say is "there is an unspecified value which is greater than the difference between a function and a given value L, where that difference is greater than zero" The problem is, I don't see any need for L or f(x) to be anywhere near one another.

For example: f(5)==>25 ;

limx=>6 f(x) = 20

-1000 < |f(5) - 20| < 1000

And

0 < |5-6| < 2

That is, I see no specific reason to even bother putting in the correct values. How does the definition define anything if we require prior knowledge of what our limits and x values are? Furthermore, how are epsilon and delta even related? The visual explanations make even less sense -- why can't we choose two given values of f(x) and L to which the difference is large, yet select a large enough epsilon so that the centre of f(x) and L lies between the bands of epsilon.

I'm terribly confused as everyone can probably tell... sorry.