Dictionary

That which is normal or typical.

Example: Unemployment is the norm in this part of the country.

A rule that is enforced by members of a community.

Example: Not eating your children is just one of those societal norms.

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

A function, generally denoted v\mapsto\left|v\right| or v\mapsto\left\|v\right\|, that maps vectors to non-negative scalars and has the following properties:

To endow (a vector space, etc) with a norm.