SPUG: Stick Riddle

Jonathan Gardner jgardn at alumni.washington.edu
Mon Jan 6 22:24:48 CST 2003

On Friday 03 January 2003 10:37, Michael R. Wolf wrote:
> infintessimally small is not zero
> infintessimally small is infintessimally small
> You're playing with Zeno's Paradox, except that you seem to be working
> with a mortise (and possibly a tenon?) instead of a tortoise and
> Achilles (but not a tendon!), and are therefore barking up the tree
> that bore the fruits known as integral calculus.

It is true that infinitessimally small is zero.

Let me explain.

The chance of having the mathematical stick break in exactly one spot is one 
divided by the number of spots you can divide the stick at.

There are an infinite number of points you can break the stick at.

We can't divide any number by infinity and get a number we understand (we're 
calling this number "infinitessimally small", but we really should call it "1 
divided by infinity").

We have take the limit as the number of spots you can divide the stick at 
approaches infinity and see what the number tends towards. This is written in 
English as "the limit of 1 over x as x approaches inifinity".

This is most definitely zero. There is no other number that this approaches. 
Therefore, our number "infinitessimally small", which I prefer to call "1 
divided by infinity", is indeed zero.

You're right, the idea of limits and finding numbers you can't normally find 
is the basis of calculus.

Now what does this have to do with perl? I don't know. Anyone care to explain?

Jonathan Gardner

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