/sci/ - Science & Math

>>8696348
There's no problem with it.

You're only being trolled if you accept the >implication that if some graph in R^n converges pointwise w.r.t. the Euclidean norm to some other graph, then they must be the same.
That's a wrong intuition and probably comes form one learning calculus/analysis where one mostly just learns about limits where the error terms always end up going to zero.

With the circle and the square, the iterative process of flipping corners and generating more and more edges, for example, never removes the jumps in derivatives - in fact, with each iteration, smoothness becomes less. The process never results in a graph that shares the properties of the circle (e.g. constant curvature).

You may use another norm, such as those used in analysis of differential equations (the stuff Terrence Tao does, to drop a name), which detects this. Pic related.