The triangle inequality is a fundamental result in mathematics that formalizes the intuitive notion that the shortest path between two points in a space is the “straight” line between them. It has multiple definitions based on the space considered and the concept of distance used including Normed Space, [[euclidean-space]], [[knowledge-mathematics-analysis-functional-analysis-metric-spaces]] and Measure Space.
In a normed vector space \(V\) one of the defining properties of the norm us the triangle inequality \[\|u+v\|\leq\|u\|+\|v\|\]for all \(u,v\in V\).