Triangle inequality

English

Proper noun

1. Template:Lb The inequality that states that the magnitude of the sum of two vectors is less than or equal to the sum of the magnitudes of the vectors.

   $\Vert 𝐱+𝐲\Vert \le \Vert 𝐱\Vert +\Vert 𝐲\Vert$

2. Template:Lb The inequality that states that the distance between two points is less than or equal to the sum of the distances between the first two points and some third point.

   $d(x,z)\le d(x,y)+d(y,z)$

3. Template:Lb Either of the above two inequalities, considered as one of the axioms which a function must satisfy to be a norm or metric respectively.

Translations

• Chinese: Template:T
• Finnish: Template:T
• French: Template:T
• German: Template:T
• Hebrew: Template:T
• Italian: Template:T
• Japanese: Template:T
• Polish: Template:T
• Portuguese: Template:T
• Romanian: Template:T (def. form)
• Russian: Template:T
• Spanish: Template:T
• Swedish: Template:T+