norm

That which is normal or typical

• In Japan, it's the norm.

  Tatoeba · davidb · CC BY 2.0 FR

• Mary lives outside the norms of society.

  Tatoeba · sundown · CC BY 2.0 FR

A rule that is imposed by regulations and/or socially enforced by members of a community

A required level of achievement

A sentence with non-descriptive meaning, such as a command, permission, or prohibitionrare

if v ne 0 then ‖v‖ ne 0 — A function which satisfies a particular set of formal conditions, created to generalize the notion of the length of a vector. Formally, a real-valued function on a vector space, generally denoted v↦|v| or v↦‖v‖, that satisfies the following propertiesrare

given a scalar k, ‖kv‖=|k|·‖v‖, where |k| is the absolute value of k — A function which satisfies a particular set of formal conditions, created to generalize the notion of the length of a vector. Formally, a real-valued function on a vector space, generally denoted v↦|v| or v↦‖v‖, that satisfies the following propertiesrare

given two vectors v,w, ‖v+w‖<‖v‖+‖w‖ (the triangle inequality) — A function which satisfies a particular set of formal conditions, created to generalize the notion of the length of a vector. Formally, a real-valued function on a vector space, generally denoted v↦|v| or v↦‖v‖, that satisfies the following propertiesrare

Any of several generalizations of the above: a field norm, ideal norm, etcrare

Any of several generalizations of the above: a field norm, ideal norm, etc.; An element of the image of some (generalized) norm, the element then said to be from the norm in question, or from the structure which gave rise to the normrare

A high level of performance in a chess tournament, several of which are required for a player to receive a titlerare