Some treatments of axiomatic set theory prefer to do without this, and instead treat the above statement not as an axiom but as a definition of equality.

Some only claim a few religious details to be axiomatic.

* Mostowski, Andrzej ( 1950 ) " Some impredicative definitions in the axiomatic set theory ," Fundamenta Mathematicae 37: 111-24.

Some results in constructive set theory use the axiom of countable choice or the axiom of dependent choice, which do not imply the law of the excluded middle in constructive set theory.

Some meals are communal, such as fondue, where a pot is set in the middle of the table for each person to dip into.

Some modern historians theorize that Nero's decision to kill Agrippina was prompted by her plotting to set Gaius Rubellius Plautus ( Nero's maternal second cousin ) or Britannicus ( Claudius ' biological son ) on the throne.

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

Some have suggested that the title " Acts " be interpreted as " The Acts of the Holy Spirit " or even " The Acts of Jesus ," since 1: 1 gives the impression that these acts were set forth as an account of what Jesus continued to do and teach, Jesus himself being the principal actor.

Some such stories are exaggerations of actual events ; others are completely fictional tales set in a familiar setting, such as the American Old West, or the beginning of the Industrial Revolution.

Some critics have also analyzed the use of alleged front organizations and conflicted patient " advocacy " groups funded by pharmaceutical companies that seek to set the mental health agenda, including the use of the law to force people to take antipsychotics against their will, often justified by claims about risk of violence.

Some mathematicians, especially in set theory, do not consider the sets and to be part of the relation, and therefore define a binary relation as being a subset of x, that is, just the graph.

Some companies such as Topdeck Travel were set up to specifically use buses to drive the hippie trail or travel to places like north Africa.

Some competitions use a " set " scoring system, with the first to seven points awarded a set in a best-or-three or best-of-five set match.

Some authors require in addition that μ ( C ) < ∞ for every compact set C. If a Borel measure μ is both inner regular and outer regular, it is called a regular Borel measure.

Some believe that Georg Cantor's set theory was not actually implicated by these paradoxes ( see Frápolli 1991 ); one difficulty in determining this with certainty is that Cantor did not provide an axiomatization of his system.

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 CPU designs compile the instruction set to a writable RAM or FLASH inside the CPU ( such as the Rekursiv processor and the Imsys Cjip ), or an FPGA ( reconfigurable computing ).

Orthographic conventions treat clitics in different ways: Some are written as separate words, some are written as one word with their hosts, and some are attached to their hosts, but set off by punctuation ( a hyphen or an apostrophe, for example ).

Some short stories set in the Anno Dracula universe have also included Carmilla.

Some content-control software includes time control functions that empowers parents to set the amount of time that child may spend accessing the Internet or playing games or other computer activities.

Some modern statistical analysis software such as PSPP still present their data in the classical data set fashion

Some theories have been put forward that the anthropocentric belief in animism among early humans was the basis for the later evolution of religions.

Some theories connect these flows directly, implying that there is significant upwelling of dense deep waters within the Southern Ocean, transformation of these waters into light surface waters, and a transformation of waters in the opposite direction to the north.

Some philosophers who have had more noteworthy theories are Parmenides, Leucippus, Plato, Aristotle, Augustine, Plotinus, Aquinas, Descartes, Spinoza, Leibniz, Hegel, Heidegger, and Sartre.

Some scholars disagree, and have proposed other theories.

Some grand unified theories of particle physics also predict that a single proton can decay, changing the baryon number by one ; however, this has not yet been observed under experiment.

Some take the approach of looking for coherent justifications of established copyright systems, while others start with general ethical theories, such as utilitarianism and try to analyse policy through that lens.

Some scholars argue that conspiracy theories once limited to fringe audiences have become commonplace in mass media, contributing to conspiracism emerging as a cultural phenomenon in the United States of the late 20th and early 21st centuries, and the possible replacement of democracy by conspiracy as the dominant paradigm of political action in the public mind.

Some research carried out at the University of Kent, UK suggests people may be influenced by conspiracy theories without being aware that their attitudes have changed.

" Some historians have put forward the idea that more recently the United States has become the home of conspiracy theories because so many high-level prominent conspiracies have been undertaken and uncovered since the 1960s.

Some of these QM theories offer descriptions of phenomenal consciousness, as well as QM interpretations of access consciousness.

Some argue that consequentialist and deontological theories are not necessarily mutually exclusive.

Some virtue ethicists hold that consequentialist theories totally disregard the development and importance of moral character.

Some theories assume the name “ Amper ” river may derive from the Celtic word for “ water ”.

Some first-order theories are algorithmically decidable ; examples of this include Presburger arithmetic, real closed fields and static type systems of ( most ) programming languages.

Some have noticed the conflicting themes that occur often throughout Qoheleth's thoughts and presented a few theories.

Some workers in the field have also attempted to formulate hidden variable theories that exploit loopholes in actual experiments, such as the assumptions made in interpreting experimental data, although no theory has been proposed that can reproduce all the results of quantum mechanics.

Some economic theories have been developed that support the idea of expanding or shrinking a money supply as economic conditions warrant.

Some notable observed features of galaxy structure ( including our own Milky Way ) that astronomers wish to explain with galactic formation theories include ( but are certainly not limited to ) the following:

Some theories in this field have now become widely accepted, but it is still an active area in astrophysics.

Some grand unified theories predict the existence of magnetic monopoles.

Some GUT theories like SU ( 5 ) and SO ( 10 ) suffer from what is called the doublet-triplet problem.

Some scholars consider the epic poem On the Nature of Things by Lucretius to present in one unified work the core arguments and theories of Epicureanism.

Some authors reject both the French and Goidelic theories and instead suggest that the ultimate source both for the Norman French, Scots and Goidelic variants of this word are to be found in a common Norse root.