Talk:Length function

The axioms for the length function correspond to that of a norm for a vector space. Indeed, for a vector space viewed as an Abelian group (with group operation being vector addition), every norm on this vector space corresponds to a length function. The connection to the concept of a metric is made in just the same way that it is made with a norm. Note also that the symmetry requirement of a metric would likely mean that the group on which the length function is defined is Abelian. Undsoweiter (talk) 04:26, 14 March 2022 (UTC)