Unemployment is the norm in this part of the country.
noun A rule that is imposed by regulations and/or socially enforced by members of a community.
Not eating your children is just one of those societal norms.
noun A sentence with non-descriptive meaning, such as a command, permission, or prohibition.
noun 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 properties: if v≠0 then ‖v‖≠0; given a scalar k, ‖kv‖=|k|⋅‖v‖, where |k| is the absolute value of k; given two vectors v,w, ‖v+w‖≤‖v‖+‖w‖ (the triangle inequality).
noun if v≠0 then ‖v‖≠0;
noun given a scalar k, ‖kv‖=|k|⋅‖v‖, where |k| is the absolute value of k;
noun given two vectors v,w, ‖v+w‖≤‖v‖+‖w‖ (the triangle inequality).
noun 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 norm.
A quaternion algebra (a,b) over ksplits if and only if b is a norm from the field extension k(a)/k, i.e. if and only if there is some x in k(a) which has field norm exactly equal to b.