Both of these theorems are only known to be true by reducing them to a computational search which is then verified by a computer program.

Both of these theorems give sufficient but not necessary conditions for the existence of all ( co ) limits of type J.

Both of those theorems were known for centuries before Dandelin, but he made it easier to prove them.

Both appeared, alongside several other important theorems, in a well-known paper by József Beck.

Both of these systems are essential for the production, development, and use of the National Forests.

Both terms anti-Semitism and antisemitism are in common use.

Both TRAM and DIEP / SIEP use the abdominal tissue between the umbilicus and the pubis.

Both use the term simply to mean a swift strategic knockout.

Both the Official IRA and Provisional IRA had established " no-go " areas for the British Army and RUC in Derry through the use of barricades.

Both the first method for cladistic analysis and the school of taxonomy originated in the work of the German entomologist Willi Hennig, who referred to it as " phylogenetic systematics " ( also the title of his 1966 book ); the use of the terms cladistics and clade was popularized by other researchers.

Both countries share the use of English and French as the two official languages as well as memberships in the Francophonie and the Commonwealth.

Both the United States and European Union have limits to nitrogen oxide emissions, which necessitate the use of a special catalytic converter or treatment of the exhaust with urea ( see AdBlue ).

( Both Canadian and British English use balloted and profiting.

Both are valued for their abrasion resistance, and hence find use in applications such as the wear plates of crushing equipment in mining operations.

Both languages now use the modern ( Congolese ) names.

Both batch and continuous distillations can be improved by making use of a fractionating column on top of the distillation flask.

Both are well familiar with the DBMS product and use its user interfaces ( as well as usually other tools ) for their work.

Both companies use extensive salt evaporation pans that have essentially diked the entire southern end of the Dead Sea for the purpose of producing carnallite, potassium magnesium chloride, which is then processed further to produce potassium chloride.

Both releases use the same NTSC Region 0 discs made from telerecordings of the original videotapes.

Both sides recognised the legitimacy and rightness, as expressions of the same faith, of the Assyrian Church's liturgical invocation of Mary as " the Mother of Christ our God and Saviour " and the Catholic Church's use of " the Mother of God " and also as " the Mother of Christ ".

Both are extremely old, going back at least to the third century, and are the oldest extant liturgies continually in use.

Both natural and social sciences use working hypotheses that are testable by observation and experiment.

Both of those systems, not coincidentally, use game mechanics inspired by D & D, giving Gamma World characters six ability scores, and measuring character development through increases in character class level.

Both retained the rights to use OS / 2 and Windows technology developed up to the termination of the agreement ; Windows NT, however, was to be written anew, mostly independently ( see below ).

Both Windows Server 2003 x64 and Windows XP Professional x64 Edition use identical kernels.

Both methods have long been promoted on the basis of lowest cost, though neither of these measurements directly, or reliably, reflects HDL particle functionality to remove cholesterol from atherosclerotic plaque and can therefore be misleading, especially on an individual patient-by-patient basis Labs use the routine dextran sulfate-Mg < sup > 2 +</ sup > precipitation method with ultracentrifugation / dextran sulfate-Mg < sup > 2 +</ sup > precipitation as reference method.

Such cells, tissues and organs would neither trigger an immune response nor require the use of Immunosuppressive drugs Both basic research and therapeutic development for serious diseases such as cancer, heart disease and diabetes, as well as improvements in burn treatment and reconstructive and cosmetic surgery, are areas that might benefit from such new technology.

Both programs allow for basic nutrient solution preparation although HydroBuddy provides added functionality to use and save custom substances, save formulations and predict electrical conductivity values.

Both came into widespread use by psychiatry, but there were grave concerns and much opposition on grounds of basic morality, harmful effects, or misuse.

Both communism and some kinds of socialism have also upheld the notion that private ownership of capital is inherently illegitimate.

Both of these notable works lent great initial support for the notion that leadership is rooted in characteristics of the leader.

Both Kūkai and Saichō aimed to connect state and religion and establish support from the aristocracy, leading to the notion of ' aristocratic Buddhism '.

Both the notion of atavism, and Haeckel's recapitulation theory, are saturated with notions of evolution as progress, as a march towards greater complexity and superior ability.

Both approaches define the same notion of sum, and the latter does so without making any separate definition for an empty sum.

Thus the Governor-General hit upon the notion to name the outpost Nueva ( meaning new Ecija ). Both the New and Old Ecija were washed by navigable rivers-the former, by Rio Grande de Pampanga and the latter, by the river Genil.

Both the Mahāvibhāṣa and the Abhidharmakośa have the notion of the intermediate state lasting " seven times seven days " ( i. e. 49 days ) at most.

Both uses of this notion can be found, and in many cases the distinction is simply ignored, see for instance examples for the first and second meaning, and an unclear definition.

Both definitions coincide in case P ( X ) is irreducible over K, which is the case used to define the notion of a separable extension of K.

Both of these perceived threats are based on the notion of the exclusion of the majority language speakers.

Both of these processes are based on the notion that people within the same group are interconnected and share successes and failures and therefore experience more sympathy towards each other than to out-group members, or social outsiders.

Both songs on the record are based on the satirical notion that all punk bands are talentless and juvenile.

Both 2: 4 and 5: 1 introduce elements of the creation story, and Davies and Allison feel it is likely that this verse is linked into the notion of a new genesis.

* Both the notion of " partnership " in the form of a senior emperor and several junior co-emperors ( usually, but not necessarily, his sons ), and Diocletian's titulature, but mainly versed in Greek ( e. g. Sebastos for Augustus, a literal translation ), became quite common is the Eastern Roman Empire, i. e. Byzantium, which lasted a further millennium after the fall of the Western Empire.

Both rejected the notion of a sham conversion to Christianity as harmful to Christianity and the State, though, in line with Enlightenment values, neither precluded the idea of more civil rights for unconverted Jews.