(adsbygoogle = window.adsbygoogle || []).push({}); Small question concerning limits' definition

Hello,

Every time I encounter the formal definition of a limit, namely :

"For every ε>0 there is some δ>0 such that, for all x, if 0 < |x - a| < δ, then |f(x) - l| < ε"

I always wonder why we need to write the left bound ( 0 < ) for the |x - a| and not for the |f(x) - l|. I'd tend to think that we should either put it for both or for neither (since it's an absolute value it's pretty obvious that it's going to be >0).

- Maybe it's to specify that |x - a| must never equal to 0?

- The δ inequality is intuitively >0 because of the ε one so there's no need to write it.

I truly have no idea.

Thank you :)

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# Small question concerning limits definitation

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