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.

The latter definition is evident in the title of David Rusk's book Cities Without Suburbs ( ISBN 0-943875-73-0 ), which promotes metropolitan government.

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.

The former proof seems applicable to a statutory merger or consolidation, the latter to a contractual acquisition.

During the latter days of November to the day of Brown's execution, it seems that most Rhode Islanders did not concur in `` E. B.'s '' suggestion.

The latter king seems to have fought a sea battle against 32 kings who had gathered against him.

The regent-mother Oghul Qaimish ( the " Camus " of William of Rubruck ) seems to have received and dismissed him with presents and a letter for Louis IX, the latter a fine specimen of Mongol insolence.

This suggestion has been recently repeated by Jerome Murphy-O ' Connor: " It is difficult to imagine that an Alexandrian Jew ... could have escaped the influence of Philo, the great intellectual leader ... particularly since the latter seems to have been especially concerned with education and preaching.

The latter course seems to have been seldom adopted ; the ordinary mode of inflicting the punishment was simply this: the censors in their new lists omitted the names of such senators as they wished to exclude, and in reading these new lists in public, quietly omitted the names of those who were no longer to be senators.

There are two separate sections of the work dedicated to Clement ( 5, 11 and 6, 6 ), the of latter which seems decidedly out of place, and Valesius argued that this was evidence that Eusebius never revised his work.

He seems to have regarded the latter as trifling, a leisure activity.

The latter hypothesis seems the more plausible evolution determinant as the surface area of the head is minute compared to the remainder of the body, thus the energy required in producing long hair for the express purpose of " optical " amplification of UV light reflected from the snow seems counterproductive ( however, it's very likely that the trait was sustained due to a nuanced combination of multiple influences, given that human hunting-skills and ingenuity were such by 50, 000 years ago that said benefits in terms of ' comfort ' could have alternatively been derived from constructing head and ear warmers of fur from prey, etc .).

While the former claim may or may not have some basis in reality, the latter seems improbable.

The latter issue seems to be very much open.

This latter point seems in particular to follow from the astonishing relation which the known six planets observe in their distances from the Sun.

" Copernicus was aware of the practice of exchanging bad coins for good ones and melting down the latter or sending them abroad, and he seems to have drawn up some notes on this subject while he was at Olsztyn in 1519.

The latter seems to have been anything but discreet in manifesting her gratitude to Pausanias, according to Justin's report: he says that the same night of her return from exile she placed a crown on the assassin's corpse and erected a tumulus to his memory, ordering annual sacrifices to the memory of Pausanias.

The film was also known as The Warriors in the USA, and The Black Prince in the UK although the latter seems to have been a working title.

While Valaquenta is not a narrative, neither is the Quenta chapter Of Beleriand and its Realms, and Tolkien never seems to have considered presenting the latter as an independent section.

There are numerous traditional and sport climbing routes in region ;, although the latter seems to be more dominant.

It seems that the purpose of this arrest was to prevent him from opposing the sentence of divorce which Cranmer pronounced in May, or the coronation of Anne Boleyn which followed on 1 June, for Fisher was set at liberty again within a fortnight of the latter event, no charge being made against him.

There are other theories, from a sudden death to a range of legends that talk of Orosius ’ s final arrival in Hispania and his founding of a monastery near to Cabo de Palos where he ended his days, although this latter idea now seems improbable.

Bhaga: Savitr seems sometimes to be identified with Bhaga also, unless the latter word is here only an epithet of Savitr.

Following the Gallic wars, Marcellus seems to drift from the historical radar until the year 216 BC, ushering in the latter part of his life.

Interpreters have debated whether the latter claim makes sense: it seems to imply that we know at least one thing about the thing in itself ( i. e., that it is unknowable ).

An effort was made yesterday in the Lackawanna courts to have the license of a successful applicant transferred to Wilkes, but it seems the latter ’ s bad reputation has followed him from Plymouth to Scranton, for the transfer was opposed by Joseph O ’ Brien, Esq., who was supposed to represent Bishop O ’ Hara in the case although the identity of his client was not made known.