Although the description sitting-on ( graph 1 ) is more abstract than the graphic image of a cat sitting on a mat ( picture 1 ), the delineation of abstract things from concrete things is somewhat ambiguous ; this ambiguity or vagueness is characteristic of abstraction.

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 many scholars today consider the Treatise to be Hume's most important work and one of the most important books in Western philosophy, the critics in Great Britain at the time did not agree, describing it as " abstract and unintelligible ".

As a result of this method, care must be taken in the interpretation of Ferguson's three factors, as factor analysis will output an abstract ' factor ' whether an objectively real factor exists or not .< reF > SAS ( R ) 3. 11 Users Guide, Multivariate Analysis: Factor Analysis Although replication of the Nationalism factor was inconsistent, the finding of Religionism and Humanitarianism had a number of replications by Ferguson and others.

Although he reserved a distaste for abstract and dogmatic religions founded around personality cults, he was attracted to the type of people he met at the Golden Dawn.

Although these examples offer alternate strategies for achieving the same abstraction, they do not fundamentally alter the need to support abstract nouns in code-all programming relies on an ability to abstract verbs as functions, nouns as data structures, and either as processes.

Although the term " abstract expressionism " was first applied to American art in 1946 by the art critic Robert Coates, it had been first used in Germany in 1919 in the magazine Der Sturm, regarding German Expressionism.

Although it is true that spontaneity or the impression of spontaneity characterized many of the abstract expressionists works, most of these paintings involved careful planning, especially since their large size demanded it.

Although Hinduism is commonly represented by such anthropomorphic religious icons such as murtis, aniconism is equally represented with such abstract symbols of God such as the Shiva linga and the saligrama.

Although Gurdjieff presents these abstract ideas as preparatory material for an exercise, the exercise itself does not appear in the text, which ends in an ellipsis during an explanation of the peculiarities of air's role in Earth's planetary composition.

Although this seems to contradict our earlier definition, we have to consider that in the abstract world our input can be arbitrarily large.

Although Newman's paintings appear to be purely abstract, and many of them were originally untitled, the names he later gave them hinted at specific subjects being addressed, often with a Jewish theme.

Although computers can play some abstract strategy games better than any human, the best Havannah-playing software to date plays quite weakly compared to human experts.

Although such results are always likely to be controversial, and working intensively with a single animal always incurs the risk of Clever Hans effects, Pepperberg's work has strengthened the argument that humans do not hold the monopoly on the complex or semicomplex use of abstract communication.

Although the algebra exists as a purely abstract construction, it can be most easily visualised in terms of operations on the edges and vertices of a dodecahedron.

Although short-lived, Rayonism was a crucial step in the development of Russian abstract art.

Although these later works have been sometimes called " philosophy ", it has been argued that there is no abstract or theoretical context to justify such a description.

Although a real pair of compasses is used to draft visible illustrations, the ideal compass used in proofs is an abstract creator of perfect circles.

Although this term historically was derived from the notion of a ring ideal of abstract algebra, it has subsequently been generalized to a different notion.

Although Wright occasionally designed art glass using stylized forms from nature, the designs of the Robie House art glass are simply abstract geometric forms.

Although one-sided flux distributions may seem somewhat abstract, they have a surprising number of applications ranging from the refrigerator magnet through industrial applications such as the brushless AC motor and magnetic coupling, to high-tech applications such as wiggler magnets used in particle accelerators and free electron lasers.

Although Hinduism is commonly represented by such anthropomorphic religious murtis, aniconism is equally represented with such abstract symbols of God such as the Shiva linga and the saligrama.

Although sometimes described as expressionistic, Auerbach is not an expressionist painter.

Although he still didn't speak to anyone, he grew fond of saying, `` The future lies in Asia '', when the opportunity arose, and when he graduated from high school his parents sent him to New York to give him a foundation, they said, for his life in Asian studies.

Although founded as a preparatory and vocational school by Amos G. Throop in 1891, the college attracted influential scientists such as George Ellery Hale, Arthur Amos Noyes, and Robert Andrews Millikan in the early 20th century.

Although it serves as a rival to Confucianism, a school of active morality, this rivalry is compromised and given perspective by the idiom " practise Confucianism on the outside, Taoism on the inside.

Although the initial certificate is available to anyone with a high school education, the diploma is meant to be a post-graduate qualification and in fact can be incorporated into a Master's degree program.

Although rules for the high school, college, and NFL games are generally consistent, there are several minor differences.

Although Ralph did not want his son to follow in his footsteps, Earnhardt would not be persuaded to give up his dream of racing, dropping out of school to race.

Although the terms " educational psychology " and " school psychology " are often used interchangeably, researchers and theorists are likely to be identified as educational psychologists, whereas practitioners in schools or school-related settings are identified as school psychologists.

Although his expulsion would have formally taken effect on 4 January 1831, Galois quit school immediately and joined the staunchly Republican artillery unit of the National Guard.

Although, strictly speaking, U. S. film director D. W. Griffith was not part of the montage school, he was one of the early proponents of the power of editing — mastering cross-cutting to show parallel action in different locations, and codifying film grammar in other ways as well.

Although prior to the introduction of compulsory school attendance laws, most childhood education occurred within the family or community, homeschooling in the modern sense is an alternative in developed countries to attending public or private schools.

Although plans to raise the school leaving age to 15 in the 1940s were never ratified, increasing numbers stayed on beyond elementary education and it was eventually raised to 16 in 1973.

Although the school was a single institution, it was divided into two parts: a grammar school called the collège or schola privata and an advanced school called the académie or schola publica.

Although educated at a Jesuit school and preparing an ecclesiastical career, he eventually converted to Protestantism and from 1687 worked as a civil law notary in Nuremberg.

Although numerous political references to the " Wizard " appeared early in the 20th century, it was in a scholarly article by Henry Littlefield, an upstate New York high school history teacher, published in 1964 that there appeared the first full-fledged interpretation of the novel as an extended political allegory of the politics and characters of the 1890s.

Although a lead vocalist named O ' Dean was auditioned, Lee had known Vince Neil from their high school days at Charter Oak High School in Covina, California and the two had performed in different bands on the garage band circuit.

Although most native speakers do not notice this, in most English dialects the " c / k " sounds in these words are not identical: in cat and kit the sound is aspirated, while in school and skill it is unaspirated ( listen to U. S. pronunciations of and ).

Although he grew up in a middle class Jewish family, Altenberg eventually separated himself from his family of origin by dropping out of both law and medical school, and embracing Bohemianism as a permanent lifestyle choice.

Although the evidence for the story is doubtful, it was immortalised at the school with a plaque unveiled in 1895.

Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of argument as universally valid.

Although he loved reading and learning, he found school to be confining and began to hate having anyone in authority over him.

Although Orbison recorded and wrote standard structure songs before " Only the Lonely ", he claimed never to have learned how to write them: " I'm sure we had to study composition or something like that at school, and they'd say ' This is the way you do it ,' and that's the way I would have done it, so being blessed again with not knowing what was wrong or what was right, I went on my own way .... So the structure sometimes has the chorus at the end of the song, and sometimes there is no chorus, it just goes ... But that's always after the fact — as I'm writing, it all sounds natural and in sequence to me.

Although he was small in primary school, he grew rapidly around the age of 12, reaching his full adult height of 6 ft 2 inches ( 188 cm ) at 18.