Math Curiousity...an old fashioned approach Message #12 Posted by Hal Bitton in Boise on 13 Jan 2009, 1:53 a.m., in response to message #1 by Don Shepherd
I put x^y=y^x into the numerical solver, and plugged various values of x in. For integer values of x>1, the solver seemed to be able to arrive at a viable solution that approached 1 (from the right) as x increased. Futhermore, for even integer values of x, there seemed to also be a viable negative solution for y, which approached 1 (from the right) as x increased. Mathematically it seems to make sense, but I admit I would be at a loss to prove it algebraically.
I wonder if someone could explain to me what the "W" variable was in Egan's solution of x^y=y^x, as that might help me see the light.
Best regards, Hal
