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Math — Limits (Epsilon–Delta)

The formal definition of a limit.

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\forall \varepsilon > 0,\ \exists\, \delta > 0

0 < |x - a| < \delta \Rightarrow |f(x) - L| < \varepsilon

\lim_{x\to a} f(x) = L

\text{Cauchy: } |a_m - a_n| < \varepsilon