ISO/TC 211 Multi-Lingual Glossary of Terms (MLGT)

Note to entry: A measure "${\displaystyle d}$ " is positive if ${\displaystyle d(x,y)>0}$ for every ${\displaystyle x,y}$ where ${\displaystyle x\ne y}$ and ${\displaystyle d(x,x)=0}$ . A measure "${\displaystyle d}$ " is symmetric if ${\displaystyle d(x,y)=d(y,x)}$ for every ${\displaystyle x,y}$ . A measure "${\displaystyle d}$ " satisfies the triangular inequality if ${\displaystyle d(x,y)\le d(x,a)+d(a,y)}$ for every ${\displaystyle a}$ , ${\displaystyle x}$ and ${\displaystyle y}$ . All numeric or vector valued attributes have such a metric, the most common being the Euclidean metric based on the square root of the sum of the squares of the differences in each dimension. Other non-Euclidean metrics take "curvature of space" into account (such as along the surface of the spheroid).