Say I want to compute a covnex hull of given points on the plane. I would like to write an algorithm, that only compares the points and doesn't do any arithmetic operations. Wikipedia states, that:
The standard $\Omega(n \log n)$ lower bound for sorting is proven in the decision tree model of computing, in which only numerical comparisons but not arithmetic operations can be performed; however, in this model, convex hulls cannot be computed at all.
Why is it so? I can't find any justification for it anywhere, I know it to be intuitively true, but how come it's a necessity?