4 ms·
What are the different limiting values for a^b (a->0, b->0) considering all paths in the a-b plane? If there are as many points generated as are generated by co
by gugagore 9y ago
What are the different limiting values for a^b (a->0, b->0) considering all paths in the a-b plane? If there are as many points generated as are generated by considering only "Manhattan" paths, then I think it's appealing to think of it as a sequence of single-variable limits.
- thaumasiotes 9y agoThe figure in https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero#Continuous_exponents https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero#Cont... strongly suggests that all nonnegative real numbers are limit points of the function f(x,y) = x^y as (x,y) approaches (0,0). It explicitly states that 0, 0.5, 1, and 1.5 are all limit points.