01/09/2008, 10:58 PM

I may have found a disproof of my exponential factorial conjecture. The exponential factorial satisfies: and , whereas the inverse function satisfies: and , which is kind of an Abel-like functional equation, but not. Now if we plug x=0 into this equation we get which would indicate that which indicates that thus disproving my conjecture.

Although this is very convincing, I'm still not convinced, since it assumes the function is invertible. I'm not sure, maybe this is proof enough. Another reason I don't think this proves it is that it assumes certain properties of from the beginning.

If my conjecture is correct, then and , so the inverse would satisfy and . This would mean the above expression with x=0 would be: which is also true. Sadly I'm not sure which of these to believe, but if it is a matter of choice, I would chose the later, since it is so much more interesting.

Andrew Robbins

Although this is very convincing, I'm still not convinced, since it assumes the function is invertible. I'm not sure, maybe this is proof enough. Another reason I don't think this proves it is that it assumes certain properties of from the beginning.

If my conjecture is correct, then and , so the inverse would satisfy and . This would mean the above expression with x=0 would be: which is also true. Sadly I'm not sure which of these to believe, but if it is a matter of choice, I would chose the later, since it is so much more interesting.

Andrew Robbins