05 Nov 07
Originally posted by PalynkaWhat is nicer, n!=1x2x...xn or sqrt(2*Pi*n)*((n^n)/(e^n))?
I don't think it's as nice as the other result. After all, with i^i you have an answer that isn't complex so, in that sense, I find it an elegant result.
Of course, "nice" is not a mathematical term. 🙂
05 Nov 07
Originally posted by geniusWhat does that have to do with anything?
What is nicer, n!=1x2x...xn or sqrt(2*Pi*n)*((n^n)/(e^n))?
The answer to this second problem requires an expression that depends on i, while the first one has an answer defined in Real numbers. That's the difference.
+-(1 + i)/sqrt(2) doesn't seem much different than leaving it as sqrt(i).
05 Nov 07
Originally posted by Palynkathe first looks nice, visually, while the second is much easier to see the value churned out, and easier to work with. They are approximatly equal, for large n.
What does that have to do with anything?
The answer to this second problem requires an expression that depends on i, while the first one has an answer defined in Real numbers. That's the difference.
+-(1 + i)/sqrt(2) doesn't seem much different than leaving it as sqrt(i).