12/21/2007, 08:40 PM

For complex z, the function z^(1/z) has an essentialy singularity at z=0. For real x, using the primary branch of roots for positive x, the function x^(1/x) goes to 0 from the right. But it's indeterminate from the left, because we're taking a negative number to various fractional and even irrational powers, which forces complex numbers and never gives us a consistent complex argument, even though the modulus consistently goes to infinity.

Either way, dx^(1/dx) must be indeterminate.

Either way, dx^(1/dx) must be indeterminate.

~ Jay Daniel Fox