v 7.00.00
23 Jan 2024
updated 23 Jan 2024

Old math


The concept of limit is essential to the complementary processes of differentiation and integration that constitute the theory of modern of calculus.

Let f(x) be a function defined on the interval containing x=a

THEN [lim x->a] f(x) = L

IF for every number epsilon >0

there exists a real number delta >0

SO THAT IF 0 < |x-a| < delta THEN |f(x) – L| < epsilon

I’d like to say “Click here and skip the ads” for Tom Lehrer’s tongue-in-cheek choice of topic, but unfortunately it’s not in the public domain, as far as I know.

The words and music are by Tom Lehrer. The song appears in the American Mathematical Monthly 81 (1974), 612.

There's A Delta For Every Epsilon (Calypso).

There's a delta for every epsilon,
It's a fact that you can always count upon.
There's a delta for every epsilon
And now and again,
There's also an N [L].

But one condition I must give:
The epsilon must be positive
A lonely life all the others live,
In no theorem (A delta for them.)

How sad, how cruel, how tragic,
(How pitiful, and other adjec-
tives that I might mention.)
The matter merits our attention.
If an epsilon is a hero,
Just because it is greater than zero,
It must be mighty discouragin'
To lie to the left of the origin.

This rank discrimination is not for us,
We must fight for an enlightened calculus,
Where epsilons all, both minus and plus,
Have deltas
To call their own.