The triangle inequality $$||x+y||\leq ||x|| + ||y||$$ is possibly the earliest inequality that we learn. Starting from high school, we learn that the shortest distance between two points is a single straight line, and if we want to travel the same distance by two or more straight lines, we will travel longer. We know very well that the triangle inequality that we so intuitively get is not limited only to the 2D or 3D spaces that we can visualize, but to…