) If formulated in von Neumann – Bernays – Gödel set theory, the surreal numbers are the largest possible ordered field ; all other ordered fields, such as the rationals, the reals, the rational functions, the Levi-Civita field, the superreal numbers, and the hyperreal numbers, are subfields of the surreals ; it has also been shown that the maximal class hyperreal field is isomorphic to the maximal class surreal field.

Certain transcendental functions can be carried over to the surreals, including logarithms and exponentials, but most, e. g., the sine function, cannot.

The surreals also contain all transfinite ordinal numbers reachable in the set theory in which they are constructed.

( Strictly speaking, the surreals are not a set, but a proper class.

The definition and construction of the surreals is due to John Horton Conway.

Most countries in this second category share the difficulty of having many of the structures of a modern political and social system without the modern standards of performance required to make them effective.

The two systems share both history and many doctrines, and the variety of the history of Christian theology, Arminianism is relevant to Calvinism ( or Reformed theology ).

The Jōmon share many physical characteristics with Caucasians, but Brace says that they are a separate genetic stock.

Members of this genus share many characteristics and uses with members of the closely related genus Celosia.

A player may trade in as many shares as he owns, but may not trade in one share of the acquired chain for half a share of the acquiring chain.

Although most cultural systems of astrology share common roots in ancient philosophies that influenced each other, many have unique methodologies which differ from those developed in the West.

In contrast to bacterial pathogens, these apicomplexan parasites are eukaryote and share many metabolic pathways with their animal hosts.

They also punished those who had too large a share of the ager publicus, or kept too many cattle on the state pastures.

Ancient Nubia shared many aspects of its mythology with ancient Egypt and there is debate about the original source of some religious concepts that the two cultures share and, whether the assimilation was from Nubia to Egypt, the reverse, or through continuing exchanges.

There are many variants of backgammon, most of which share common traits.

Although there are many people who identify as being into BDSM who don't share the experience with anyone besides play-or sexual partners, " BDSM " is also used to denote a subculture of people interested in BDSM who may socialize together, educate each other, and throw " play parties " at which BDSM activities are welcome.

Languages seem to share certain properties although many of these include exceptions.

Though there are many important differences of interpretation and opinion of the Bible on which Christianity is based, Christians share a set of beliefs that they hold as essential to their faith.

While many Chadians may share that assessment, the uprising appears to be a power struggle within the elite that has long controlled Chad.

Several major North American drainage basins and many minor ones share a common border with the Columbia River's drainage basin.

Although all administrative links with Jamaica were broken in 1962, the Cayman Islands and Jamaica continue to share many links and experiences, including membership in the Commonwealth of Nations ( and Commonwealth citizenship ) and a common united church ( the United Church in Jamaica and the Cayman Islands ) and Anglican diocese ( although there is debate about this ) as well as a common currency ( until 1972 ).

Vasea of Cyprus are broadly divided into two main ethnic communities, Greek Cypriots and Turkish Cypriots, who share many customs but maintain distinct identities based on ethnicity, religion, language, and close ties with their respective motherlands.

They share many similarities with the higher plants, including the presence of asymmetrical flagellated cells, the breakdown of the nuclear envelope at mitosis, and the presence of phytochromes, flavonoids, and the chemical precursors to the cuticle.

At the foundation of the new rule, they were called Hermits of St Damiano, or Moronites ( or Murronites ), and did not assume the appellation of Celestines until after the election of their founder to the Papacy as Celestine V. The fame of the holy life and the austerities practised by the hermit in his solitude on the Mountain of Majella, near Sulmona, attracted many visitors, several of whom were moved to remain and share his mode of life.

In these cases, expansion buses are entirely separate and no longer share any architecture with their host CPU ( and may in fact support many different CPUs, as is the case with PCI ).

In many homes an empty place setting is symbolically left at the table for the Baby Jesus or, for a lonely wanderer who may be in need of food, or if a deceased relative should come and would like to share in the meal.

The living tradition which we share draws from many sources:

In fact, Italian and French share many more root words in common that do not even appear in Spanish.

The many types of indexes share the common property that they reduce the need to examine every entry when running a query.

Any two black holes that share the same values for these properties, or parameters, are indistinguishable according to classical ( i. e. non-quantum ) mechanics.

Due to its arrangement, groups, or columns, and periods, or rows, of elements in the table either share several chemical properties, or follow a certain trend in characteristics such as atomic radius, electronegativity, etc.

The properties of the chemical elements are often summarized using the periodic table that organizes the elements by increasing atomic number into rows (" periods ") in which the columns (" groups ") share recurring (" periodic ") physical and chemical properties.

The properties of the chemical elements are often summarized using the periodic table, which powerfully and elegantly organizes the elements by increasing atomic number into rows (" periods ") in which the columns (" groups ") share recurring (" periodic ") physical and chemical properties.

Polyenes and dienes, share many of their properties.

Glass-ceramic materials share many properties with both non-crystalline glass and crystalline ceramics.

According to this view, " after observing a long run of red on the roulette wheel, for example, most people erroneously believe that black will result in a more representative sequence than the occurrence of an additional red ", so people expect that a short run of random outcomes should share properties of a longer run, specifically in that deviations from average should balance out.

Hyperbolas share many of the ellipses ' analytical properties such as eccentricity, focus, and directrix.

Isomers share a chemical formula but normally have very different properties because of their different structures.

Group 12 elements are usually considered to be transition metals ; however, zinc ( Zn ), cadmium ( Cd ), and mercury ( Hg ) share some properties of both groups, and some scientists believe they should be included as main group elements.

There are approximately 7, 000 current human languages, and many, if not most seem to share certain properties, leading to the hypothesis of Universal Grammar, as argued by the generative grammar studies of Noam Chomsky and his followers.

The members of the two classes share similar properties and are given both a common name ( such as sarin ) and a two-character NATO identifier ( such as GB ).

Programming languages share properties with natural languages related to their purpose as vehicles for communication, having a syntactic form separate from its semantics, and showing language families of related languages branching one from another.

In mathematics, profinite groups are topological groups that are in a certain sense assembled from finite groups ; they share many properties with their finite quotients.

In integrated circuits, the desirable properties of MOSFETs allowed them to capture nearly all market share for digital circuits.

The theory suggests that linguistic ability manifests itself without being taught ( see poverty of the stimulus ), and that there are properties that all natural human languages share.

This effect is the basis for the code division multiple access ( CDMA ) property of DSSS, which allows multiple transmitters to share the same channel within the limits of the cross-correlation properties of their PN sequences.

Both Book Antiqua and Arial ( the alternative for Helvetica ) share the original typefaces ' character width, spacing and kerning properties.

* Topological manifolds share the local properties of Euclidean spaces and are therefore also all locally compact.

In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes ; members of the same conjugacy class share many properties, and study of conjugacy classes of non-abelian groups reveals many important features of their structure.

These modes share many properties, such as synchronization and / or frequencies and grey / color level correspondence.