Anon05/01/26, 14:46No.16968462
Calculus depends on uncountable sets to produce interesting results; the Lebesgue integral of [math]f:[0,1]\to\{0,1\}; x\in\mathbb Q\mapsto0, x\notin\mathbb Q\mapsto1[/math] is [math]1[/math].So in some sense, "quantized" behaviour is analytically irrelevant.What does that imply then for physics and physical limits? As I understand it, there is some minimal unit, the Planck length, in which physics can happen. Then, how does a path integral work, when a particle can only occupy a finite amount of spaces between any two points?