norm

Etymology 1

From French norme, from Old French, from Latin norma (“a carpenter's square, a rule, a pattern, a precept”).

noun

1. That which is normal or typical.
   Unemployment is the norm in this part of the country.
   […] the world needs a constitutional moment that will generate new institutions and actuate a new norm. 2008, Dennis Patterson, Ari Afilalo, The New Global Trading Order: The Evolving State and the Future of Trade
   "This shocking report proves once again that we urgently need a radical shake-up of hospital care," said Jeremy Hughes, chief executive of the Alzheimer's Society. "Given that people with dementia occupy a quarter of hospital beds and that many leave in worse health than when they were admitted, it is unacceptable that training in dementia care is not the norm." December 16, 2011, Denis Campbell, “Hospital staff 'lack skills to cope with dementia patients'”, in Guardian
   Projects such as the King's Cross refurbishment, Waterloo blockade, Scottish electrification and the Borders show that the industry can do wonderful work - but that must become the norm, not the exception. December 18 2019, Richard Clinnick, “Railway's 2020 vision”, in Rail, page 3
2. 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.
   Peer pressure helps explain why people in Europe weigh less than Americans: They follow different social norms, like eating only at mealtimes instead of snacking throughout the day. 2011, Roy F. Baumeister, John Tierney, Willpower, page 230
3. (philosophy, computer science) A sentence with non-descriptive meaning, such as a command, permission, or prohibition.
4. (mathematics) A function, generally denoted v↦|v| or v↦‖v‖, that maps vectors to non-negative scalars and has the following properties:
   1. if v ne 0 then ‖v‖ ne 0;
   2. given a scalar k, ‖kv‖=|k|·‖v‖, where |k| is the absolute value of k;
   3. given two vectors v,w, ‖v+w‖<‖v‖+‖w‖ (the triangle inequality).
5. (chess) A high level of performance in a chess tournament, several of which are required for a player to receive a title.

Etymology 2

Back-formation from normed.

verb

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