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Im trying to figure out what the difference is between the following two epsilon delta statements and the kinds of functions they satisfy:

For all real numbers x and for all delta>0, there exists epsilon>0 such that |x|<delta implies |f(x)|<epsilon

vs.

there exists delta>0 such that for all epsilon>0 and for all real numbers x, |x|<delta implies |f(x)|<epsilon

I'm just very confused about the whole epsilon delta thing. I looked online and found the definition of a limit and tried to understand what part epsilon and delta played in the definition, but things like the FOR ALLs and the apparent importance of order in the definition are confusing me as to what exactly they're trying to say.

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# Homework Help: Epsilon Delta definitions?

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