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Undefined * Undefined = Undefined

We know that infinity divided by infinity is undefined:

= Undefined

If you are interested, here is the proof.

As I stated in my previous proof, most people would immediately stop working on an equation if they had undefined anywhere in the equation... but not me. Here is even more confusion with undefined.

First, we know that this is true:

∞ = ∞ * ∞

If we substitute this equation into the numerator of the first equation, then we would get:

∞ * ∞

= Undefined

This fraction can then be split into two fractions like this:


= Undefined

If we substitute the very first equation twice in this new equation, then we would get this equation:

Undefined * Undefined = Undefined

Again, this may seem obvious, yet I have never seen undefined defined like this before.

by Phil for Humanity
on 07/10/2011

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