such that

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 Cornell 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 definition:

◇ Cauchy’s “flaw”: ambiguous

Finding a certain

too counter-intuitive to grasp the idea by most university math students.

◇ **Intuitive Alternative**:

Find **any** 2 natural numbers m (“**Start**“), k (“**Scale**“) such that:

**A Simple Analogy in Life**:

Let P(n) = Any Person’s lifespan of age n

m = ‘Start’ Age to retire, say 60

k = ‘Scale’ of interval (in years, eg. 1 year)

A = Limit of a person’s lifespan, say 80 (male) or 85 (female)

As we grow older (n increases), from a certain “Start” point (m), our lifespan P(n) approaches the limit A, plus or minus k/n (years).

Reblogged this on Singapore Maths Tuition.