0^0 is Undefined
What does 0^0 equal?
Some people think 0^0 equals 1, while other people think 0^0 is undefined. Here is a simple proof to answer this mystery.
Take the natural log or ln of both sides of the equation:
Since ln (a^b) = b * ln a, then this is true:
When x is greater than or less than zero (x != 0), then (ln x) is a number (n), so this is true:
If we apply Euler's number (e) to both sides of the equation, this would be the result:
Simplified, this is:
Therefore, if we substitute this equation into the original assumption., then we would have proved:
Thus, any non-zero number to the zeroth power equals 1.
However, when x is equal to zero (x=0), then (ln x) is (ln 0), and this equation is undefined.
Since we had this equation above:
We can substitute to this equation when x is equal to 0.
Therefore, we must stop working on this equation. As a result:
by Phil for Humanity