The latter definition ignores the direction of the vectors and thus describes the angle between one-dimensional subspaces and spanned by the vectors and correspondingly.

" With the latter definition, Confucianism is religious, even if non-theistic, in the sense that it " performs some of the basic psycho-social functions of full-fledged religions ", in the same way that non-theistic ideologies like Communism do.

The difference between the two definitions is that under the former, finite sets are also considered to be countable, while under the latter definition, they are not considered to be countable.

") A large segment of the technical community insist the latter is the " correct " usage of the word ( see the Jargon File definition below ).

In the latter case, the disease may only be defined as a " disease " ( which by definition means an illness ) in hosts who secondarily become ill after contact with an asymptomatic carrier.

This broader definition distinguishes open content from open source software, since the latter must be available for commercial use and adaptation by the public.

The latter definition is necessary, because there are logically true but logically unknowable propositions such as " Nobody knows that this sentence is true ":

One may think of potential energy as being derived from force or think of force as being derived from potential energy ( though the latter approach requires a definition of energy that is independent from force which does not currently exist ).

Alexander VII's Apostolic Constitution Sollicitudo Omnium Ecclesiarum laid out the doctrine of the Immaculate Conception of the Blessed Virgin Mary in terms almost identical to those utilized by Pope Pius IX when he issued his infallible definition Ineffabilis Deus and the former work is cited in footnote 11 of the latter.

This stem-based definition is equivalent to the more common definition of Sauropsida, which Modesto and Anderson synonymized with Reptilia, since the latter is more well known and more frequently used.

The latter definition comes from the fact that the path to water is the whole way of life in an arid desert environment.

Should a legal distinction be necessary between a ( location ) channel as defined above and a television channel in this sense, the terms " programming service " ( e. g. ) or " programming undertaking " ( for instance, ) may be used instead for the latter definition.

: Two political Sects have arisen within the U. S. the one believing that the executive is the branch of our government which the most needs support ; the other that like the analogous branch in the English Government, it is already too strong for the republican parts of the Constitution ; and therefore in equivocal cases they incline to the legislative powers: the former of these are called federalists, sometimes aristocrats or monocrats, and sometimes tories, after the corresponding sect in the English Government of exactly the same definition: the latter are stiled republicans, whigs, jacobins, anarchists, disorganizers, etc.

The classic definition of Italian Fascism applies to the latter part of the history of the movement in power, when Italy was firmly under the leadership of Benito Mussolini.

With the latter definition, convex hulls may be extended from Euclidean spaces to arbitrary real vector spaces ; they may also be generalized further, to oriented matroids.

Note that the definition is somewhat ambiguous because the user of a program can be another program and, if the latter is a portion of the set of program that is required to be interoperable, it might well be that it does need to have knowledge of the characteristics of other units.

This latter definition is commonly used in audio distortion ( percentage THD ) specifications.

The latter definition distinguishes hallucinations from the related phenomena of dreaming, which does not involve wakefulness.

The latter is the function in the definition.

The latter definition distinguishes hallucinations from the related phenomena of dreaming, which does not involve wakefulness ; illusion, which involves distorted or misinterpreted real perception ; imagery, which does not mimic real perception and is under voluntary control ; and pseudohallucination, which does not mimic real perception, but is not under voluntary control.

This latter definition was made official in 2009 by geographic boards of Canada and the United States.

This latter property is usually taken as the definition of the derivative.

Conservative Judaism holds that both Reform and Reconstructionist Judaism have made major and unjustifiable breaks with historic Judaism, both by their rejection of Jewish law and tradition as normative, and by their unilateral acts in creating a separate definition of Jewishness ( i. e. the latter movement's acceptance of patrilineal descent as an additional way of defining Jewishness.

As it is, they consider that the North is now reaping the fruits of excess egalitarianism, that in spite of its high standard of living the `` American way '' has been proved inferior to the English and Scandinavian ways, although they disapprove of the socialistic features of the latter.

So great a man could not but understand, too, that the thing that moves men to sacrifice their lives is not the error of their thought, which their opponents see and attack, but the truth which the latter do not see -- any more than they see the error which mars the truth they themselves defend.

The latter is not reduced to the former.

This strange person quarrels with a cyclist because the latter is using the path rather than the highroad.

However, it is important to trace the philosophy of the French Revolution to its sources to understand the common democratic origin of individualism and socialism and the influence of the latter on the former.

Analogously, anyone who argues that Einstein's theory of gravitation is simpler than Newton's, must say rather more to explain how it is that the latter is mastered by student-physicists, while the former can be managed ( with difficulty ) only by accomplished experts.

In the latter research program, information is available for 2,758 Cornell students surveyed in 1950 and for 1,571 students surveyed in 1952.

Nogaret is hardly an impartial witness, and even he did not make his charges against Boniface until the latter was dead, but there is some truth in what he said and more in what he did not say.

And, after becoming the right-hand man of Enver Pasha, he is sent by the latter to pave the way for a new Turkish Empire embracing `` the union of all Turks throughout Central Asia from Adrianople to the Chinese oases on the Silk Trade Route ''.

The latter is what concerns us all.

The latter is likely to occur when the thyroid is removed.

and it is still very far from certain how valid the party's claim is that in `` a growing number of kolkhozes '' the peasants are finding it more profitable, to surrender their private plots to the kolkhoz and to let the latter be turned into something increasingly like a state farm.

The location of the latter now is determined for tax purposes at the time of registration, and it is now accepted practice to consider a motor vehicle as being situated where it is garaged.

The latter matter is considered in detail in a later section.

This latter reaction is in accord with the reported decomposition of Af.

Data on the former are scanty, but there can be little doubt that the latter is sometimes born at a length greater than that of any of the others, thereby lending support to the belief that the anaconda does, indeed, attain the greatest length.

the former figure is based on a somewhat unusual birth of four by a Central American female ( see chapter on Laying, Brooding, Hatching, and Birth ), the latter on a `` normal '' newly born individual.

Andrew's report to his sovereign, whom he rejoined in 1251 at Caesarea in the Palestine, appears to have been a mixture of history and fable ; the latter affects his narrative of the Mongols ' rise to greatness, and the struggles of their leader Genghis Khan with Prester John ; it is still more evident in the position assigned to the Mongols ' homeland, close to the prison of Gog and Magog.

Others have suggested dissociation can be separated into two distinct forms, detachment and compartmentalization, the latter of which, involving a failure to control normally controllable processes or actions, is most evident in DID.

This cultural exchange was evident in literature through the introduction of German courtly poetry, or Minnesang, in the latter part of the 13th century.

The latter are evident mainly in the center of the country and create what is commonly called the Central Valley ( Valle Central ) between them and the Andes.

When it became evident, in mid-July 1794, that Robespierre and Saint-Just were planning to strike against their political opponents Joseph Fouché, Jean-Lambert Tallien, and Marc-Guillaume Alexis Vadier – the latter two were members of the Committee of General Security – the fragile truce within the government was dissolved.

Of particular importance to the development of folk rock were the subtle folk influences evident in such Beatles ' compositions as " I'll Be Back ", " Things We Said Today ", and " I'm a Loser ", with the latter song being directly inspired by folk singer-songwriter Bob Dylan.

During his schoolyears Thomas the younger became firmly attached to the latter church ; he eventually developed a dislike for the Roman Catholic Church that became evident in later years.

There are evident Gallicanisms in the Ambrosian Rite, but so there are in the present Roman, and the main outlines of the process by which they arrived in the latter are sufficiently certain, though the dates are not.

It later became evident that Shaw himself had no idea what Sammartino had concocted, the latter having called for the referee to stop the bout after Shaw caught him in a bear hug that Sammartino could easily have broken.

That the latter theorems have much to say about all of mathematics and more controversially, about a range of philosophical issues ( e. g., Lucas 1961 ) is less than evident.

The latter role was made evident during the episode hosted by Oprah Winfrey in spring of 1986 where in the cold opening, Vance played Lorne Michaels ' personal slave ( who was actually supposed to be the character Celie from the movie The Color Purple ) who convinces Michaels to force Oprah into performing stereotypically black roles by beating her, only to have Oprah choke Lorne in a headlock while opening the show with " Live from New York, it's Saturday Night !".

This latter act was particularly evident over December 1999, counting down to January 1, 2000.

The creation of model company towns was particularly evident in Britain during the latter half of the nineteenth century with the creation of Saltaire, Bournville, Port Sunlight, Creswell and New Earswick, and coincided with the housing reform movement which emphasised the improvement of housing for the working class.

Percussionist Laudir de Oliveira, with Chicago since 1973, decided to explore other options and would leave the band in 1981, realizing that the Latin percussion evident in the latter half of the previous decade no longer fit the band's style.

This point was evident through the large bronze bust of Twain, which sat just west of the State Capitol in the lobby of The Union ’ s latter building at 301 Capitol Mall.

The influence of the latter is particularly evident in comparing Bauer's 1917 work Three Impressions for piano to Griffes's Roman Sketches published a year earlier: each is an impressionistic-style suite with a poem preceding each movement.

The Ravads influence on Jonathan of Lunel also is evident, though the latter did not attend his lectures.

Their evident and increasingly destabilizing influence was disturbing to many less extreme revolutionary politicians, including leading Montagnard figures such as Georges Danton and Maximilien Robespierre-the latter of whom especially disapproved of the Hébertists ' atheism.

She is notably multilingual, competent in French and Chinese, as well as being a fluent English speaker ; the latter being evident in her Western education, her interest in Queen and the Chronicles of Narnia, and also by having an all-English speaking role as Angela Burton in Genshiken.

However, by the end of Manuel's reign, the strains of constant warfare on all fronts and the Emperor's various grandiose projects had become evident: the historian Nicetas Choniates attributes the rise of piracy in the latter years of Manuel's reign to the diversion of the funds intended for the maintenance of the fleet for other needs of the imperial treasury.

By the latter rounds, Sanchez's expertise was becoming more evident, as he repeatedly shook Laporte with blows to the head.

The book was finished and published by officials of the U. S. State Department to advanvce an obvious political agenda, and the angry, pugnacious tone of its latter chapters betray Stuart's self-effacing modesty and refined manners evident in the first seven chapters.

There is in the hadith an evident miracle of the Prophet's due to his proclamation of the Negus's death on the same day that the latter died in Axum.

Rusi Modi was evidently an accumulator of runs, this fact being evident from his test average of 46 and a first-class average of 53, which also weighed a lot on paper when seen alongside his 20 centuries in the latter respect.