Determine all possible positive real triplets (a, b, c) satisfying a^b =c; b^c = a and c^a = b

(In reply to re: Cyclical by brianjn)

0^0 is undefined. Some approximation through limits (all from the right, from the left a lot of problems arise)
lim (x^x,x->0) = 1
lim (0^x,x->0) = 0
lim (x^0,x->0) = 1

Another way of looking at it:
0^0 = 0^(0*-1) = (0^0)^-1 = 1/(0^0)
0^0 = 0^(0*2) = (0^0)^2
which would have a unique solution of 0^0 = 1.

For most applications this works, but actually it is not defined. Check also this page.

Posted by Robby Goetschalckx on 2007-06-08 09:54:37