Since this holds true when performing addition on any real numbers, we say that " addition of real numbers is an associative operation.

In addition to his office, the archbishop also holds a number of other positions ; for example, he is Joint President of the Council of Christians and Jews in the United Kingdom.

Given any expression involving complex numbers, bras, kets, inner products, outer products, and / or linear operators ( but not addition ), written in bra-ket notation, the parenthetical groupings do not matter ( i. e., the associative property holds ).

For example, Roman Catholic hermeneutics holds that there are many senses in which the Bible is true in addition to literal truth.

In addition to wins, Young still holds the major league records for most career innings pitched ( 7, 355 ), most career games started ( 815 ), and most complete games ( 749 ).

Another view holds that Apollo was a fairly recent addition to the Greek pantheon coming originally from Lydia.

In addition to holding the Apostles ', the Nicene and the Athanasian Creeds of the universal church, it also holds to the confessions of its predecessor bodies.

Critical scholarship generally holds to the two-source hypothesis as most probable, which argues that the author used the Gospel of Mark and the hypothetical Q document in addition to unique material, as sources for the gospel.

In addition it holds exhibitions as well as concerts and other events.

In addition to classes and a monthly dance mixer, the group also holds an annual Victorian Ball.

The Catholic Church recognizes that the addition of " and the Son " to the Greek form of the Creed would be wrong, because of the specific meaning of the Greek verb that is translated as " proceeds ", but it holds that both forms of the text, with and without " Filioque ", are orthodox in other languages, where " proceeds " can also represent a different Greek verb, used by Greek Fathers when saying that the Holy Spirit " proceeds " ( in that sense ) from the Son.

In addition to the textured surface and hand holds, the wall may contain surface structures such as indentions ( incuts ) and protrusions ( bulges ), or take the form of an overhang, underhang or crack.

In addition, during NPC sessions the Chinese leadership holds press conferences with foreign reporters, and this is one of the few opportunities Western reporters have of asking unscripted questions of the Chinese leadership.

The transfer principle states that true first order statements about R are also valid in * R. For example, the commutative law of addition, x + y = y + x, holds for the hyperreals just as it does for the reals ; since R is a real closed field, so is * R. Since for all integers n, one also has for all hyperintegers H. The transfer principle for ultrapowers is a consequence of Łoś ' theorem of 1955.

One of Kim Jong-il's sons, in addition to his North Korean citizenship, holds Portuguese citizenship from the time he lived in Macau.

In addition, the majority of each party's membership holds membership in both parties.

In addition, the South African Legion holds a street collection to gather funds to assist in welfare work among military veterans.

In addition to the main campus in Ruston, Louisiana Tech holds classes at the Louisiana Tech University Shreveport Center, Cyber Innovation Center in Bossier City, and Barksdale Air Force Base.

In addition to the career steals record, Henderson also holds the single-season record for stolen bases ( 130 in 1982 ) and is the only player in AL history to steal 100 bases in a season, having done so three times.

In addition, the 1995 – 96 squad holds several other records, including the best road record in a standard 41-road-game season ( 33 – 8 ), the all-time best start by a team ( 41 – 3 ), the longest home winning streak ( 44 games, 7 from previous season ), and the best start at home ( 37 – 0 ).

An addition increased the square footage from 23, 700 to 53, 500 and now holds a book collection of almost 200, 000 volumes.

In addition to the annual Fourth of July parade, the PWCA holds an annual meeting in October, where the PWCA usually provides a forum for officials running for elective office.

Ross Noble holds the record for most appearances as a panelist, with 13 ( in addition to one extra appearance as team captain ).

The networks for military communications are one of the best examples of networks which not only must be changed with the changes in objectives but also must be changed with the addition of new machines of war.

In addition, his definition of a tragedy invites our attention, because a serious and important action may very well be one that tests the moral fiber of the author or of the characters.

In addition one serum was obtained from a donor ( R. E. ) who had been sensitized 6 years previously.

Since emotional reactions in the higher vertebrates depend on individual experience and are aroused in man, in addition, by complex symbols, one would expect that the hypothalamus could be excited from the cortex.

Two very useful ways for modifying a form-dictionary are the addition to the dictionary of complete paradigms rather than single forms and the application of a single change to more than one dictionary form.

During the poetically sterile years he was writing novels at the rate of almost one a year and was, in addition, burdened with bad health ( he spent six months in bed in 1881, too ill to do more than work slowly and painfully at A Laodicean ).

It appears that an Orthodox girl in the community disrupted plans for an outing sponsored by one of the Jewish service groups because she would not travel on Saturday and, in addition, required kosher food.

In addition, several styles of music exist as the known arabo-andalous, one of the singers Chaoui style is Salim Hallali.

Acid-base conjugate pairs differ by one proton, and can be interconverted by the addition or removal of a proton ( protonation and deprotonation, respectively ).

In addition to this standard variety, in everyday life most Austrians speak one of a number of Upper German dialects.

* Melanchrus-he was overthrown sometime between 612 BC and 609 BC by a faction that, in addition to the brothers of Alcaeus, included Pittacus ( later renowned as one of the Seven Sages of Greece ); Alcaeus at that time was too young to be actively involved ;

Alfred's military reorganisation of Wessex consisted of three elements: the building of thirty fortified and garrisoned towns ( burhs ) along the rivers and Roman roads of Wessex ; the creation of a mobile ( horsed ) field force, consisting of his nobles and their warrior retainers, which was divided into two contingents, one of which was always in the field ; and the enhancement of Wessex's seapower through the addition of larger ships to the existing royal fleet.

These operations are compounding ( or the addition of one idea onto another, such as a horn on a horse to create a unicorn ); transposing ( or the substitution of one part of a thing with the part from another, such as with the body of a man upon a horse to make a centaur ); augmenting ( as with the case of a giant, whose size has been augmented ); and diminishing ( as with Lilliputians, whose size has been diminished ).

In addition, ASU is ranked 78th in the world / 45th in the US by the Academic Ranking of World Universities and was named as one of " America's Best College Buys " by Forbes magazine.

One must be careful here ; for instance, some analyses count an addition of two numbers as one step.

According to the special theory of relativity, the aberration looks as a transform of the celestial sphere due to different frames of reference and is virtually a special case of velocity addition, namely one of the light beam and frames ' relative velocity v. The formula from relativistic aberration can be simplified to

In addition, a 2010 Cochrane Collaboration review of trials of Risperidone, one of the biggest selling antipsychotics and the first of the new generation to become available in generic form, found only marginal benefit compared with placebo and that, despite its widespread use, evidence remains limited, poorly reported and probably biased in favor of risperidone due to pharmaceutical company funding of trials.

During the extended peak of the strip, the workload grew to include advertising, merchandising, promotional work, public service comics and other specialty work — in addition to the regular six dailies and one Sunday strip per week.

In addition, Jason Alexander, who performed as Pseudolus in one scene in Jerome Robbins ' Broadway, also won a Tony for Best Actor in a Musical.

In one common challenge students are divided into groups and given a quantity of wood sticks, a distance to span, and glue, and then asked to construct a bridge that will be tested to destruction by the progressive addition of load at the center of the span.

The complement of aircraft carried by the Minas Gerais included at one point six Grumman S-2E antisubmarine planes, in addition to several SH-3D Sea King helicopters and Aérospatiale Super Puma and HB-350 Esquilo helicopters.

The phrase ' advanced composites ' in FRP construction may indicate the addition of carbon fibre, kevlar ( tm ) or other similar materials, but it may also indicate other methods designed to introduce less expensive and, by at least one yacht surveyor's eyewitness accounts, less structurally sound materials.

For one thing they had too good an opinion of their own ability ... Another point was their faulty field dispositions, and in addition there was rampant indiscipline and inexperience displayed ...

Zosimus consistently refers to the migrants as " Scythians " ( unlike Ammianus, who refers to them as " Goths "), specifically stating at one point that, in addition, " Goths, Taifali and other tribes " were involved.