Although Cantor himself defined the set in a general, abstract way, the most common modern construction is the Cantor ternary set, built by removing the middle thirds of a line segment.

Although most of Chopin's nocturnes are in an overall ternary form, quite often the individual sections ( either the A, the B, or both ) are in binary form, most often of the asymmetrical variety.

Although the United States and the U.S.S.R. have been arguing whether there shall be four, five or six top assistants, the most important element in the situation is not the number of deputies but the manner in which these deputies are to do their work.

Although they are forbidden to sit with the customers, the dancers are sometimes proffered drinks, and most of them can bolt one down in mid-shimmy.

Although modern scholars have expressed surprise that `` the simple magic square of three '', a mere `` mathematical puzzle '', was able to exert a considerable influence on the minds and imaginations of the cultured Chinese for so many centuries, they could have found most of the answers right within the square itself.

Although Tylor undertook a field trip to Mexico, both he and Frazer derived most of the material for their comparative studies through extensive reading, not fieldwork, mainly the Classics ( literature and history of Greece and Rome ), the work of the early European folklorists, and reports from missionaries, travelers, and contemporaneous ethnologists.

Although most species are associated with water and damp habitats, some are specialised to live in trees and in deserts.

Although in many frog species, females are larger than males, this is not the case in most species where males are actively involved in territorial defence.

Although they are often considered to be weeds in gardens, this viewpoint is not always necessary, as most of them die when the soil temperature warms up again in early to late spring when other plants are still dormant and have not yet leafed out.

Although most extant species of Asteraceae are herbaceous, the examination of the basal members in the family suggests that the common ancestor of the family was an arborescent plant, a tree or shrub, perhaps adapted to dry conditions, radiating from South America.

Although originally controversial, the axiom of choice is now used without reservation by most mathematicians, and it is included in ZFC, the standard form of axiomatic set theory.

Although there are variations from place to place, most of the world's architects are required to register with the appropriate jurisdiction.

Although the general direction of the mountains, ridges, and valleys is northeast and southwest, irregularity is one of the most prominent characteristics.

Although Albert has received relatively little recognition in German history, his dissolution of the Teutonic State caused the founding of the Duchy of Prussia ( and also the Hohenzollern dynasty ), which would eventually become arguably the most powerful German state and instrumental in uniting the whole of Germany.

Although the increased contact brought by trade between the Japanese and the Ainu contributed to increased mutual understanding, sometimes it led to conflict, occasionally intensifying into violent Ainu revolts, of which the most important was Shakushain's Revolt ( 1669 – 1672 ).

Although most of the members of the community signed a document issued by Hasan Ali Shah summarizing the practices of the Ismailis, a group of dissenting Khojas surprisingly asserted that the community had always been Sunni.

Although Muslim scholars have often debated over who this verse refers to, most classical commentators and modern translators have taken the opinion that this refers to Amram, the father of Moses and Aaron.

Although many other chemists have repeated this advice, IUPAC and most chemistry texts still favour the usage of allotrope and allotropy for elements only.

Although most of the legions were lost, about 10, 000 Romans cut their way through to safety, maintaining unit cohesion.

Although still actively involved in running his many businesses, Carnegie had become a regular contributor to numerous magazines, most notably the Nineteenth Century, under the editorship of James Knowles, and the influential North American Review, led by editor Lloyd Bryce.

Although early Commodore advertisements attempted to cast the computer as an all-purpose business machine, the Amiga was most commercially successful as a home computer, with a wide range of games and creative software.

Although the hardware is limited to four separate sound channels, software such as OctaMED uses software mixing to allow eight or more virtual channels, and it was possible for software to mix two hardware channels to achieve a single 14-bit resolution channel by playing with the volumes of the channels in such a way that one of the source channels contributes the most significant bits and the other the least.

Although he is sometimes regarded as among the first and most influential architects of Nordic modernism, a closer examination of the historical facts reveals that Aalto ( while a pioneer in Finland ) closely followed and had personal contacts with other pioneers in Sweden, in particular Gunnar Asplund and Sven Markelius.

Although most dialects of English used in the former British Empire outside of North America and Australasia are, to various extents, based on British English, most of the countries concerned have developed their own unique dialects, particularly with respect to pronunciation, idioms and vocabulary.

Although page flipping was a hardware possibility, the limited memory forced most applications to do all their drawing directly to the visible screen, often resulting in graphical flicker or visible redraw.

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.

Although Patchen has given previous evidence of an interest in jazz, the musical group that he works with, the Chamber Jazz Sextet, is often ignored by jazz critics.

Although the site may not contain the features themselves, there are often opportunities to include them as additional interest to the site.

Although blind students have benefited from talking calculators, the abacus is still very often taught to these students in early grades, both in public schools and state schools for the blind.

Although specialized and experienced amateur astronomers tend to acquire more specialized and more powerful equipment over time, relatively simple equipment is often preferred for certain tasks.

Although the name actually applies to a group of snakes, it is often used to refer only to one species in particular, the common or green anaconda, Eunectes murinus, which is one of the largest snakes in the world.

Although often cited as a proponent of existentialism, the philosophy with which Camus was associated during his own lifetime, he rejected this particular label.

Although the Greek word " techně " is often mistranslated as " art ," it actually implies mastery of any sort of craft.

Although the terms adiabatic and isocaloric can often be interchanged, adiabatic processes may be considered a subset of isocaloric processes ; the remaining complement subset of isocaloric processes being processes where net heat transfer does not diverge regionally such as in an idealized case with mediums of infinite thermal conductivity or non-existent thermal capacity.

Although several species are often considered weeds, people around the world value amaranths as leaf vegetables, cereals, and ornamentals.

Although its function is unknown, it has been often suggested that the jewel was one of the æstels — pointers for reading — that Alfred ordered sent to every bishopric accompanying a copy of his translation of the Pastoral Care.

Although a phoneme's allophones are all alternative pronunciations for a phoneme, the specific allophone selected in a given situation is often predictable.

Although Carolla often supports social viewpoints traditionally dominated by liberal politicians, such as his support for abortion and the legalization of marijuana, his socio-political views tend to be largely conservative or libertarian.

Although allenes often require specialized syntheses, the parent, propadiene is produced on a large scale as an equilibrium mixture with methylacetylene:

Although colors can be mixed, pigments are often not specified.

Although AVMs are often associated with the brain and spinal cord, they can develop in any part of the body.

Although he was a major figure in the protectionist wing of the Conservative Party after 1844, Disraeli's relations with the other leading figures in the party, particularly Lord Derby, the overall leader, were often strained.

Although essential amenities, such as running water, furniture and a limited ration of food were provided, luxury items were often forbidden.

Deane and J. R. Thomson write this valid conclusion, “ The Book of Obadiah is occupied with one subject – the punishment of Edom for its cruel and unbrotherly love conduct towards Judah ...” One can link this idea of punishment to one of the major prophets “ Ezekiel ” who “... interprets the exile to Babylon and the destruction of Jerusalem as deserved punishments for the sins of those who themselves committed them .” Verses 3-7 in Obadiah explain to the reader the reason for the punishment theme, “ Confidence in one ’ s power, intelligence, allies, or the topographical features of one ’ s territory is often mentioned as an attribute of those who foolishly confront the Lord and are consequently punished .” Although destruction is vital to understanding Obadiah, it is of note to understand the destruction being a consequence of action.

Although it's increasingly common for couples – particularly younger couples – to have " power neutral " relationships and / or play styles, activities and relationships within a BDSM context are often characterized by the participants ' taking on complementary, but unequal roles ; thus, the idea of informed consent of both the partners becomes essential.

Although written literature is only slowly evolving ( due to the predominance of French as the " language of the educated "), there exists a wealth of oral literature, which is often tales of kings and heroes.

Although these two are often considered interchangeable, compilers and execution environments usually assign different signals to these.

Although vulnerable to antitank fire, they can often be repaired or replaced in the field.