zero^zero is undefined

The color of the point 'P' represents the value of x^a, where 'x' is the horizontal coordinate of 'P' and 'a' is the vertical coordinate of 'P'. Red corresponds to x^a = 1 and blue corresponds to x^a = 0. You can change both 'x' and 'a' by dragging the point 'P' with your mouse or change one of the values by dragging the corresponding points on the sliders. The equations up above show the current values based on the position of 'P'. Along the x-axis, the fact that a = 0 makes x^a = 1, and the point 'P' is red. Along y-axis, the fact that x = 0 makes x^a = 0, and the point 'P' is blue. When both x = 0 and a = 0, the value of x^a is undefined, and the point 'P' is yellow. It's easiest to make both zero using the sliders. Since both red points and blue points occur arbitrarily close to the yellow point, we cannot argue that 0^0 should be either red, 0^0 = 1 or blue, 0^0 = 0 so we are forced to conclude that 'P' is undefined.