norm

1. That which is normal or typical.

   Unemployment is the norm in this part of the country.

2. A rule that is enforced by members of a community.

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

3. A sentence with non-descriptive meaning, such as a command, permission or prohibition.
4. 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:
5. A high level of performance in a chess tournament, several of which are required for a player to receive a title.

verb

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