X-files style alien head with rays spreading out from it?
No. I was exploring the exponential function. It has no zeros. There is a power series for it. If you truncate it to n-terms, the truncated series is just a polynomial and so has n zeros. The more terms you have, the closer the approximation, except that the more terms you have, the more zeros there are. Somehow, in the limit as the number of terms goes to infinity, all these zeros vanish. Where did they go?
My plan is to find out how to use the polymediator to include mathematics in my web pages, then come back and finish off this page with a proper explanation
I try it here
Wow! That seems to work. The point is that one gets a series of approximations to the exponential function.
These approximations get better and better, in the sense that if you pick a z the approximate values converge to. On the other hand, a polynomial of nth degree on the complex numbers has n zeros. The approximations are getting worse and worse in the the sense that they have too many zeros and get more and more. What is going on? Where do they all go to? What has my picture got to do with it?