Some definitions specify a self-sacrificial nature to altruism and a lack of external rewards for altruistic behaviors.

Some theorems related to compactness ( see the glossary of topology for the definitions ):

Some definitions also add that for any production rule of the form u → v of a context-sensitive grammar, it shall be true that | u |≤| v |.

Some definitions focus on the question of the probability of encountering a given condition of a system once characteristics of the system are specified.

Some definitions of epilepsy require that seizures be recurrent and unprovoked, but others require only a single seizure combined with brain alterations which increase the chance of future seizures.

Some definitions of Mersenne numbers require that the exponent p be prime, since the associated number must be composite if p is composite.

Some scientific materialists have been criticized, for example by Noam Chomsky, for failing to provide clear definitions for what constitutes matter, leaving the term ' materialism ' without any definite meaning.

Some definitions of management are:

Some authors use the term " grammatical gender " as a synonym of " noun class ", but others use different definitions for each ( see below ).

") Some critics have argued for more or fewer dimensions while others have proposed entirely different theories ( often assuming different definitions of " personality ").

Some definitions would have it that any assumption that a person's behavior would be influenced by their racial categorization is racist, regardless of whether the action is intentionally harmful or pejorative.

Some definitions of racism also include discriminatory behaviors and beliefs based on cultural, national, ethnic, caste, or religious stereotypes.

Some definitions simply refer to all forms of socialism that follow an electoral, reformist or evolutionary path to socialism, rather than a revolutionary one.

Some definitions now include acts of unlawful violence and war.

Some theorems are " trivial ," in the sense that they follow from definitions, axioms, and other theorems in obvious ways and do not contain any surprising insights.

Some definitions suggest xenophobia as arising from irrationality or unreason.

Some authors use more general definitions of " positive definite " that include some non-symmetric real matrices, or non-Hermitian complex ones.

Some common definitions include:

Some definitions simply refer to all forms of socialism that follow an electoral, reformist or evolutionary path to socialism, rather than a revolutionary one.

Some definitions of famines are:

Some definitions also set a minimum level for population density ( at least 2, 000 persons / square km ).

Some modern magicians, such as Aleister Crowley and those who follow the traditions of the Hermetic Order of the Golden Dawn and Ordo Templi Orientis, describe magic in rational terms, using definitions, postulates and theorems.

( Some definitions do not consider the second form of rule to be permitted, in which case a context-free grammar that can generate the empty word cannot be so transformed.

Some also create new terms without substantially changing the definitions of uncertainty or risk.