Undefined + Undefined = Undefined
We know that infinity divided by infinity is undefined:
| ∞ — ∞ |
= Undefined |
|---|
If you don't believe me, here is the proof.
Most people would immediately stop working on an equation if they had undefined anywhere in the equation... but not me. So, I wondered what would happen if we tried breaking down the equation above, and I think I discovered something that I've never seen before, yet I believe it is intuitively obvious if you think about it.
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:
As I said before, this seems obvious, yet I don't know of anyone who bothered proving it.
by Phil for Humanity
on 07/10/2011