Thread: 0 ^ 0 = 1

Originally Posted by vart

to calculate 0^0 one can take lim(x^y) when x,y -> 0

Depending on the relative speed of approximation to zero the result will be different

But that assumes that x and y can both be varied. If you treat y as a constant 0, then you are left with lim (x ^ 0) x->0 which is clearly 1.

In practice these undefined points can be defined in whatever way is most convenient for the problem at hand (usually, equal to the limit when approaching from the appropriate direction)