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:

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 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.

Some of the sinusoids contained large numbers of nucleated red cells, and cells of the granulocytic series were found in small numbers.

* Some irrational numbers are algebraic and some are not:

Some large telephone companies have toll-free numbers set up.

Some architectures use a particular register as an accumulator in some instructions, but other instructions use register numbers for explicit operand specification.

Some Allied officers who were acquainted with the superior numbers of the enemy, and aware of their strong defensive position, ventured to remonstrate with Marlborough about the hazards of attacking ; but the Duke was resolute – " I know the danger, yet a battle is absolutely necessary, and I rely on the bravery and discipline of the troops, which will make amends for our disadvantages ".

Some, unaware of the local terrain, ran towards the swamps where unknown numbers drowned.

Some early digital computers used an electrical model of the common decimal ( base ten ) numeral system to represent numbers internally.

Some scientists argue that megafauna cryptids are unlikely to exist undetected in great enough numbers to maintain a breeding population, and are unlikely to be able to survive in their reported habitats due to issues of climate and food supply.

Some authors use countable set to mean a set with the same cardinality as the set of natural numbers.

Some sets are infinite ; these sets have more than n elements for any integer n. For example, the set of natural numbers, denotable by, has infinitely many elements, and we cannot use any normal number to give its size.

Some even contain 00 and 000 buttons to make large numbers easier to enter.

Some models have the ability to extend memory capacity to store more numbers ; the extended address is referred to as an array index.

Some studies indicate that agricultural production and livestock numbers may only be sufficient to feed about half of the country's population.

Some youth of Generation Y have seized upon activities which they can claim as their own, and have begun rejecting more traditional sports in increasing numbers.

Some stars, such as the nearby star 82 Eridani, were named in a major southern-hemisphere catalog called Uranometria Argentina, by Benjamin Gould, and are not true Flamsteed numbers, and should properly contain a G, as in 82 G. Eridani.

Some estimates imply that practically all the matter, when measured by numbers of particles, in the visible universe ( not including dark matter ) is in the form of neutrinos, and that roughly elementary particles of matter exist in the visible universe, mostly neutrinos.

* Some numbers ( e. g., 1 / 3 and 0. 1 ) cannot be represented exactly in binary floating-point no matter what the precision.

Some Christian theologians ( particularly neo-Scholastics ) saw Cantor's work as a challenge to the uniqueness of the absolute infinity in the nature of God — on one occasion equating the theory of transfinite numbers with pantheism — a proposition which Cantor vigorously rejected.

Some lottery players will choose the same numbers every time, or intentionally change their numbers, but both are equally likely to win any individual lottery draw.

Some leading Conservatives ( e. g. Chancellor Ken Clarke ) favoured joining and insisted that Britain retain a completely free choice, whilst increasing numbers of others expressed their reluctance to join.

* Some totally disconnected groups, such as the Galois group of an infinite extension of fields, or the additive group of the p-adic numbers.

Some remarks on the purported or commonly perceived numerological significance of specific small numbers may be found at the articles on these numbers, as at 77 ( number ).