Whereas a philosophical skeptic may deny the very existence of knowledge, an empirical skeptic merely seeks likely proof before accepting that knowledge.

Whereas in the CN-case, the resulting maximal subgroups M are still Frobenius groups, the maximal subgroups that occur in the proof of the odd-order theorem need no longer have this structure, and the analysis of their structure and interplay produces 5 possible types of maximal subgroups, called types I, II, III, IV, V. Type I subgroups are of " Frobenius type ", a slight generalization of Frobenius group, and in fact later on in the proof are shown to be Frobenius groups.

* Whereas Uncle Joe concludes his proof reductio ad absurdum, modern mathematicians would more commonly claim " proof by contradiction.

Whereas the stewards of X since 1988 ( including the prior X. Org ) had been vendor organizations, the Foundation was led by software developers and used community development based on the bazaar model, which relies on outside involvement.

Whereas GreenLight relies on haemoglobin as a chromophore, water within the target tissue is the chromophore for Holmium lasers.

Whereas the stewards of X since 1988 ( including the previous X. Org, part of The Open Group ) had been vendor organizations, the Foundation is led by software developers and using community development on the bazaar model, which relies on outside involvement.

Whereas the first theme is based on a sharp dotted rhythm, the second relies on a static long-short-short pattern.

Whereas some argue that immigrants displace domestic workers, others believe this to be a fallacy, arguing that such a view relies on a belief that the number of jobs in the economy is fixed, whereas in reality immigration increases the size of the economy, thus creating more jobs.

Whereas neurofunk ( which also come from techstep ) relies on science fiction soundscape and really clean production, darkstep bring back elements of darkcore like horror movie soundtrack or vocal snippets, overdistorted techstep bassline and industrial soundscape.

Whereas the maintenance rotary fund had in the past sustained losses considerably beyond expectations, the introduction of the cost-billing system plus other control refinements has resulted in keeping the fund on a proper working basis.

Whereas the usual organic surface-active agent is strongly sorbed at oil - water interfaces, the highly charged ions are most strongly sorbed at interfaces between water and insoluble materials exhibiting an ionic structure ( see Table 26-2 on p. 1678 ).

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 Bultmann's `` center '' position is structurally inconsistent and is therefore indefensible on formal grounds alone, the general position of the `` right '', as represented, say, by Karl Barth, involves the rejection or at least qualification of the demand for demythologization and so is invalidated on the material grounds we have just considered.

Whereas the primary meanings of the Lo Shu diagram seemed to have been based on its inner mathematical properties -- and we shall see that even its secondary meanings rested on some mathematical bases -- the urgent desire to place everything into categories of fives led to other groupings based on other numbers, until an exaggerated emphasis on mere numerology pervaded Chinese thought.

Whereas Bachofen saw the switch to paternity on Athena's behalf as an increase of power, Freud on the contrary perceived Athena as an " original mother goddess divested of her power ".

Whereas the AMD K6-III + topped out at 570 MHz due to its short pipeline, even when built on the 180 nm process, the Athlon was capable of clocking much higher.

It exists in four major polymorphs: α, β, γ and T. Whereas α, β and T phases are based on B < sub > 12 </ sub > icosahedra, the γ-phase can be described as a rocksalt-type arrangement of the icosahedra and B < sub > 2 </ sub > atomic pairs.

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 cultural anthropology focused on symbols and values, social anthropology focused on social groups and institutions.

Whereas the philosophical approach to consciousness focuses on its fundamental nature and its contents, the medical approach focuses on the amount of consciousness a person has: in medicine, consciousness is assessed as a " level " ranging from coma and brain death at the low end, to full alertness and purposeful responsiveness at the high end.

Whereas stories at this time in Coronation Street were largely about family affairs, Brookside concentrated on social affairs such as industrial action, unemployment and the black market.

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 deforestation was primarily driven by subsistence activities and government-sponsored development projects like transmigration in countries like Indonesia and colonization in Latin America, India, Java, and so on, during late 19th century and the earlier half of the 20th century.

Whereas Plato's demiurge is good wishing good on his creation, gnosticism contends that the demiurge is not only the originator of evil but is evil as well.

* Whereas the notion of " free equivalence relation " does not exist, that of a free groupoid on a directed graph does.

Whereas Socrates was eventually put on trial and executed as a corrupting influence, Euripides chose a voluntary exile in old age, dying in Macedonia.

Whereas certain religions focus on individuals, like Christianity focuses on Jesus, Islam focuses solely on Allah.

Whereas immigration to Northern industrial centers had resulted in Northern control of the population-based House of Representatives, Southern politicians sought to maintain the fragile balance of power in the Senate, where each state received equal representation.

Whereas previously any noble could start a war, the monarchs of Europe of necessity consolidated military power in response to the Napoleonic war.

Whereas his father and brother had concentrated consular power largely in the hands of the Flavian family, Domitian admitted a surprisingly large number of provincials and potential opponents to the consulship, allowing them to head the official calendar by opening the year as an ordinary consul.

Whereas capitalist ( and right-libertarian ) principles concentrate economic power in the hands of those who own the most capital, libertarian socialism aims to distribute power, and thus freedom, more equally amongst members of society.

Whereas by supposing they have given up themselves to the absolute arbitrary power and will of a legislator, they have disarmed themselves, and armed him to make a prey of them when he pleases ..."

Whereas in the 17th century the commercial success of the Dutch had fuelled English resentment, in the late 18th century the growth of British power led to Dutch resentment.

Whereas Ged's quest led to his dramatic confrontation with himself and his own darkness, and ultimately, to his acknowledgment of his full identity and power, Tenar's triumph is that of coming to freedom.

Whereas the State of Qi was a major power of its era, the State of Lu played only a minor role in the politics of its time.

Whereas a Golomb code has a tunable parameter that can be any positive value, Rice codes are those in which the tunable parameter is a power of two.

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 at one point, he had the power to exile his opponents ( and, thus, eviscerate individual criticism ) to border regions of the state, he died when torn into pieces by chariots.

Whereas the British had devolved much power to local government in the 1890s, one of the Free State's first acts was to abolish many of the powers of County Councils and replace them with unelected County managers.

Whereas the utility of prospective power analysis in experimental design is universally accepted, the usefulness of retrospective techniques is controversial.

Whereas Social Statics had been the work of a radical democrat who believed in votes for women ( and even for children ) and in the nationalization of the land to break the power of the aristocracy, by the 1880s he had become a staunch opponent of female suffrage and made common cause with the landowners of the Liberty and Property Defence League against what they saw as the drift towards ' socialism ' of elements ( such as Sir William Harcourt ) within the administration of William Ewart Gladstone – largely against the opinions of Gladstone himself.

Whereas Charles I had been in part restrained by a Parliament that would not always do as he wished ( the cause of the Civil War ), Cromwell was able to wield much more power as only loyalists were allowed to become MPs, turning the chamber into a rubber-stamping organisation.

Whereas the Rig Veda expressed uncertainty and was not dogmatic, the Brahmanas express confidence in the infallible power of the mantras.

Whereas the Renaissance drew on the wealth and power of the Italian courts and was a blend of secular and religious forces, the Baroque was, initially at least, directly linked to the Counter-Reformation, a movement within the Catholic Church to reform itself in response to the Protestant Reformation.

Whereas the men's songs invoke power, the women's songs draw power away from the opposing stickball team.

Whereas Haskell exercised extensive executive control over the Oklahoma Legislature ( mainly through his force of personality ), Cruce lost much of the executive power Haskell established.

Whereas IBM's PC ( and almost all PC compatibles ) had a power supply in a corner of the main case, the PC1512's power supply was integrated with that of its monitor.

Whereas with large devices minor fluctations in the power provided through the brush mechanism are inconsequential, in the case of tiny electronic components, the brushing introduces unacceptable levels of noise in the stream of power supplied.