Sometimes, when describing the closeness of $x$ to $a$ as being less than $\delta$, it's stated as $|x-a|<\delta$ and sometimes it's stated as $0<|x-a|<\delta$.
What is the " $0<$ " part that's sometimes included in the definition, I'm a bit confused about that. Is it just telling us that the distance can't be zero?
thanks.
2026-05-06 03:15:38.1778037338
question about epsilon, delta limit definition
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The "$0 <$" part explicates the interest in a neighborhood around a point. For any desired error, there exists a nonzero deviation from the point of interest such that the function evaluated inside this neighborhood does not change by more than the desired error.