> makes you go looking for some kind of loophole. But there isn't one.
Doesn't it require fractal cuts? Seems like a loophole to me. It only seems paradoxical because you assume the resulting pieces are smooth at some scale, like real cuts are.
Doesn't it require fractal cuts? Seems like a loophole to me. It only seems paradoxical because you assume the resulting pieces are smooth at some scale, like real cuts are.
This isn’t just aesthetic. Although probability is one of the oldest areas of mathematical thought, dating back millennia, it took measure theory to put it on a really solid basis, several decades ago. These approaches are powerful and useful, but some of the corners are certainly counterintuitive.