01/30/2008, 05:09 PM
Ivars Wrote:Barrow said (not exact quote):
if x^x=1/2 has no solutions in real and complex numbers, it may lead to creation of new numbers just to fill that gap. Has anyone already tried to define such numbers?
But it has a solution in the complex numbers?
\( \frac{1}{2}=x^x \)
\( \ln\left(\frac{1}{2}\right)=x\ln(x)=e^yy \)
\( W\left(\ln\left(\frac{1}{2}\right)\right)=y=\ln(x) \)
\( x=e^{W\left(\ln\left(\frac{1}{2}\right)\right)} \)