Whereas classical arithmetic defines operations on individual numbers, interval arithmetic defines a set of operations on intervals:

Whereas microeconomics deals with individual firms, people, and other institutions that work within a set frame work of rules to balance prices and the workings of a singular government.

Whereas originally the term Navigation applies to the process of directing a ship to a destination, Navigation research deals with fundamental aspects of navigation in general.

Whereas Mars negative relates to our physical energy, Mars positive deals with our mental strength.

Whereas realism deals mainly with security and material power, and liberalism looks primarily at economic interdependence and domestic-level factors, constructivism most concerns itself with the role of ideas in shaping the international system ( indeed it is possible there is some overlap between constructivism and realism or liberalism, but they remain separate schools of thought ).

Whereas 1 Henry VI deals primarily with the loss of England's French territories and the political machinations leading up to the Wars of the Roses, and 3 Henry VI deals with the horrors of that conflict, 2 Henry VI focuses on the King's inability to quell the bickering of his nobles, the death of his trusted adviser Humphrey, Duke of Gloucester, the rise of the Duke of York and the inevitability of armed conflict.

Whereas Southern Rhodesia had seen a flood of fortune-seeking prospectors seeking to set up independent mines, Northern Rhodesia was largely untouched, and this allowed the Company to agree large scale deals with major commercial mining companies.

Whereas a redaction critic would use such intertextuality to argue for a particular order and process of the authorship of the books in question, literary criticism takes a synchronic view that deals with the texts in their final form, as an interconnected body of literature.

Whereas multiculturalism deals with cultural diversity within a particular nation or social group, cross-culturalism is concerned with exchange beyond the boundaries of the nation or cultural group.

Whereas his first solo album contained several very satirical texts, Am Ende der Sonne deals with more serious themes such as politics, social criticism and personal subjects.

Whereas the traditional IS-LM Model deals with economy under autarky ( or a closed economy ), the Mundell – Fleming model describes an open economy.

Whereas the eighteenth century had been a time in which man sought justice, the nineteenth and twentieth have been centuries in which men are satisfied with law.

Whereas the members of Jewish Christianity were circumcised and adhered to dietary laws, the Pauline Christianity featured in Acts did not require Gentiles to be circumcised or to obey all of the Mosaic laws, which is consistent with Noahide Law.

Whereas D & D merged armor with defense, BRP treated them as separate functions: the act of parrying was a defensive skill that reduced an opponent's chance to successfully land an attack, and the purpose of armor was to absorb damage.

Whereas a scalar CPU must complete the entire process of fetching, decoding, and executing each instruction and value in a set of data, a vector CPU can perform a single operation on a comparatively large set of data with one instruction.

Whereas we say X is an H-set of Z if every cover of X with open sets of Z has a finite subfamily whose Z closure contains X.

Whereas peptidoglycan is a standard component of all bacterial cell walls, all archaeal cell walls lack peptidoglycan, with the exception of one group of methanogens.

Whereas Travis's right hand used his index finger for the melody and thumb for bass notes, Atkins expanded his right hand style to include picking with his first three fingers, with the thumb on bass.

Whereas revolution is never legitimate under the divine right of kings, the philosophy associated with the Mandate of Heaven approved of the overthrow of unjust rulers.

Whereas objectivism is concerned with the " object of our knowledge ", constructivism emphasises " how we construct knowledge ".

" Whereas, say, infinitists regard the regress of reasons as " shaped " like a single line, Susan Haack has argued that it is more like a crossword puzzle, with multiple lines mutually supporting each other.

Whereas Parker started with practice and then moved to theory, Dewey began with hypotheses and then devised methods and curricula to test them.

Whereas Skyrme's example involved pion physics, there is a much more familiar example in quantum electrodynamics with a magnetic monopole.

Whereas Lang was worried about the advent of the Nazi regime, partly because of his Jewish heritage, his wife and screen writer Thea von Harbou had started to sympathize with the Nazis in the early 1930s and joined the NSDAP in 1932.

Whereas in May and June 2005 victory of the Christian Democrats seemed highly likely, with some polls giving them an absolute majority, this picture changed shortly before the election at 18 September 2005.

Whereas Simple harmonic motion oscillates with only the restoring force acting on the system, Damped Harmonic motion experiences friction.

Whereas his references to Judah are of a general kind, Ephraim or Samaria being sometimes mentioned in the same connection or more frequently alone, the situation implied throughout and the whole tone of the addresses agree with what we know of the Northern Kingdom at the time, and his references to places and events in that kingdom are so numerous and minute as to lead to the conclusion that he not only prophesied there, but that he was a native of that part of the country.

Whereas a Möbius strip is a surface with boundary, a Klein bottle has no boundary.

Whereas most economists start with the individual's perspective, Marx starts with the perspective of society as a whole.

Whereas most of the isotopes of meitnerium can be synthesized directly this way, some heavier ones have only been observed as decay products of elements with higher atomic numbers.

Whereas Dante Gabriel Rossetti, in his own commentary compares the Minotaur with all three sins of violence within the seventh circle: " The Minotaur, who is situated at the rim of the tripartite circle, fed, according to the poem was biting himself ( violence against oneself ) and was conceived in the ' false cow ' ( violence against nature, daughter of God ).

Whereas a high percentage of the regular students can be expected to read other texts which more or less plow the same ground in a little different direction, the married students chose whole books on specific areas and went into much greater detail in their areas of interest.

Whereas the written Torah has a fixed form, the Oral Torah is a living tradition that includes not only specific supplements to the written Torah ( for instance, what is the proper manner of shechita and what is meant by " Frontlets " in the Shema ), but also procedures for understanding and talking about the written Torah ( thus, the Oral Torah revealed at Sinai includes debates among rabbis who lived long after Moses ).

Whereas the older " depth scales " tried to infer the level of " hypnotic trance " based upon supposed observable signs, such as spontaneous amnesia, most subsequent scales measure the degree of observed or self-evaluated responsiveness to specific suggestion tests, such as direct suggestions of arm rigidity ( catalepsy ).

Whereas a spanking is invariably administered to the bottom, " smacking " is less specific and may refer to slapping the child's hands, arms or legs as well as its bottom.

Whereas American culture posits the notion of the " melting-pot " and cultural diversity, the expression " French culture " tends to refer implicitly to a specific geographical entity ( as, say, " metropolitan France ", generally excluding its overseas departments ) or to a specific historico-sociological group defined by ethnicity, language, religion and geography.

Whereas most of the information given in the previous books is useful in such a way that it could still be applicable today, this book is primarily concerned with the specific details about other strategies that existed at the time.

Whereas a person ’ s Gattungswesen ( human nature ) does not exist independent of specific, historically-conditioned activities, the essential nature of a human being is actualized when a man — within his given historical circumstance — is free to sub-ordinate his will to the external demands he has imposed upon himself, by his imagination, and not the external demands imposed upon him by other people.

Whereas the Enlightenment invokes a specific movement in Western philosophy, modernity tends to refer only to the social relations associated with the rise of capitalism.

Whereas the minister ’ s duty was to understand specific affairs, the ruler was responsible for correctly judging ministers ’ performances.

Whereas content may be offensive in a non-specific way, harassment directs obscenities and derogatory comments at specific individuals focusing for example on gender, race, religion, nationality, sexual orientation.

Whereas there is no general technique for constructing Lyapunov functions for ODEs, in many specific cases, the construction of Lyapunov functions is known.

Whereas some traditions were once believed across the whole of England, most belong to specific regions:

Whereas with a flap ( or tap ), a specific gesture is used to strike the active articulator against the passive one, in the case of a trill the articulator is held in place, where the airstream causes it to vibrate.

Whereas “ authority ” denotes a specific position in an established government, the term “ legitimacy ” denotes a system of government — wherein “ government ” denotes “ sphere of influence ”.

Whereas a glyph was a specific graphic shape from a particular font, whether the shape represented a single character or a set of characters.

Whereas, in times past, the bullwhip was designed for one basic, main purpose, modern whip makers design their whips for different specific purposes and to suit different throwing styles.

Whereas in the U. S. warranties are generally provided in writing subject to control of the laws, in other countries warranties may be governed by specific statutes.

Whereas ipchains and ipfwadm combine packet filtering and NAT ( particularly three specific kinds of NAT, called masquerading, port forwarding and redirection ), Netfilter separates packet operations into multiple parts, described below.

Whereas medical school teaches physicians a broad range of medical knowledge, basic clinical skills, and limited experience practicing medicine, medical residency gives in-depth training within a specific branch of medicine.

Whereas some subdivisions comprise exclusive gated communities, others are merely demarcations denoting a specific neighborhood.

Whereas a vertical GPO assists organizations in specific industries, such as health care, food service, legal, dairy, and industrial manufacturing, a horizontal GPO assists companies across a broad spectrum of industries.

Whereas the usefulness can be seen as the model being helpful for the specific purpose at hand for which the model is constructed at first place.

Whereas ribozymes can be chemically designed to target specific genes and cleave them in a sequence specific manner.