furrbear: (Geode Bear)
[personal profile] furrbear
∀ε>0 ∃δ>0 ∋ 0<|x-a|<δ⇒|ƒ(x)-L|<ε


Answer: Karl Weierstrass' Formal Definition of a Limit:

Let f be a real-valued function defined on an open interval of real numbers containing c (except possibly at c) and let L be a real number. Then

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

means that

for each real ε > 0 there exists a real δ > 0 such that for all x with 0 < |xc| < δ, we have |f(x) − L| < ε.

or, symbolically,

 \forall \varepsilon > 0 \ \ \exists \delta > 0 \ \ \forall x (0 < |x - c| < \delta \ \implies \ |f(x) - L| < \varepsilon).


[livejournal.com profile] fzks_cub was the first to respond with the words "definition of the limit"

Those who answered [livejournal.com profile] jrjarrett got the location from where I saw it correct, but missed the correct answer.
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