$latex displaystylelim_{xto a}f(x) = L

iff$

$latex forall varepsilon >0, exists delta >0 $ such that

$latex boxed{0<|x-a|<delta}

implies |f(x)-L|< varepsilon $

The above *scary* ‘epsilon-delta’ definition of “Limit” by the French mathematician Cauchy in 19th century is the standard **rigorous** definition in today’s **Analysis** textbooks.

It was not taught in my Cambridge GCE A-Level Pure Math in 1970s (still true today), but every French Baccalaureate Math student (Terminale, equivalent to JC 2 or Pre-U 2) knows it by heart. A Cornel University Math Dean recalled how he was told by his high-school teacher to memorise it — even though he did not fully understand — the “epsilon-delta” definition by “chanting”:

“for all epsilon, there is a delta ….”

(French: *Quelque soit epsilon, il existe un delta …*)

In this video, I am glad someone like Prof N. Wildberger recognised its “flaws” albeit rigorous, by suggesting another more intuitive…

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