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Page "Limit (category theory)" ¶ 56
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Both and these
Both these youths, who greatly admired Henrietta, were somewhat younger than she, as were also the neighboring Friedenwald boys, who were then studying medicine ; ;
Both of these systems are essential for the production, development, and use of the National Forests.
Both of these purposes exist side by side without much overt conflict under present conditions.
Both these types, and those in between, are in existence by reason of a legislative interest in libraries that began at Albany as early as 1950, with the creation by the legislature of county library systems financed by county governments with matching funds from the state.
Both of these replacements were political moderates and prospectively more supportive of the Commander-in-Chief.
Both these analyses require homoscedasticity, as an assumption for the normal-model analysis and as a consequence of randomization and additivity for the randomization-based analysis.
Both Algorithm I and Algorithm II compute these values correctly.
Both these popular methods are used to analyze sound and better understand the acoustic phenomenon.
Both of these are published in the Historiae Francorum Scriptores, Tome ii ( Paris, 1639 – 1649 ).
Both Stephanus and Eustathius write of these Amazons in connection with the placename Thibais, which they report to have been derived from Thiba's name.
Both of these processes were in most cases brief and formulaic, but they opened up in the possibility, if some citizen wanted to take some matter up, of a contest before a jury court.
Both these words have similar meaning, and Young's Literal Translation renders them and their derivatives as “ age ” or “ age-during ”.
Both these charges were later found to be considerably lacking in evidence ; nevertheless Pike, facing arrest, escaped into the hills of Arkansas, sending his resignation from the Confederate Army on July 12.
Both of these elastomers undergo strain crystallization.
Both these paintings share a similar formal structure that consists of an open landscape that is seen beyond and through the opening of a dark grotto.
" Both these songs appeared on the second album, Klokkenluiders van Amsterdam.
Both the F-14 Tomcat and AIM-54 Phoenix missile continue in the service of the Islamic Republic of Iran Air Force, although the operational abilities of these aircraft and the missiles are questionable, since the US refused to supply spare parts and maintenance after the 1979 revolution ; except for a brief period during the Iran-Contra Affair.
Both of these identities together imply that the associator is totally skew-symmetric.
Both stable and unstable isotopes of beryllium are created in stars, but these do not last long.
Both of these breeds have an increased ability to convert feed into lean muscle, which causes these particular breeds ' meat to have a reduced fat content.
Both of these are important in regards to the uncertainty surrounding the Beowulf manuscript, as the works which it draws from or influences suggest time-frames of composition, geographic boundaries from which it could be composed, or range ( both spatial and temporal ) of influence ( i. e. when it was " popular " and where its " popularity " took it ).
Both of these men were statesmen and public administrators in addition to their role as Christian pastors, teachers and leaders.
Both scales are open-ended at the top, and thus the upper grade of these systems is always increasing as boulderers ascend more difficult problems.
Both of these factors are strong incentives to provide effective protection and management of western / lowland bongo populations.

Both and theorems
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 theorems use the notion of a time-constructible function.
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 and give
Both parties and the Ministry of the Interior were busily at work after the elections trying to unearth the political affiliations of the successful candidates and, thereby, give the elections a confidential but known degree of national political significance.
Both techniques give the music purity and clarity.
Both hands-two dancers face each other and give hands right to left and left to right.
" Both Michael Fincke and fellow NASA Astronaut Greg Chamitoff deliver the line " Never give up ... never surrender.
Both rating agencies give a negative outlook on the debt, meaning further downgrades are possible.
Both types of plaited stitches give a subtle but interesting visual texture, and tend to draw the fabric inwards, making it stiffer.
Both types give good results, and the choice between them is personal.
Both give super human abilities to whoever eats them.
Both TiCl < sub > 4 </ sub > and TiCl < sub > 3 </ sub > give active catalysts.
Both the person accused of the crime and the accuser would give speeches based on their sides of the story.
which may be interpreted either as or as with the tensor derivative of the velocity vector Both interpretations give the same result, independent of the coordinate system — provided is interpreted as the covariant derivative.
Both authors satirise social behaviour and give characters names that express their personalities.
Both genetic ( e. g., Berardinelli-Seip congenital lipodystrophy, Dunnigan familial partial lipodystrophy ) and acquired ( e. g., HIV-related lipodystrophy in patients treated with highly active antiretroviral therapy ) forms of lipodystrophy may give rise to severe insulin resistance and many of metabolic syndrome's components.
Both forms of secondary education last three years, and give a formal qualification to enter university or ammattikorkeakoulu, i. e. Finnish polytechnics.
Both factors are broken up (" partitioned ") into their hundreds, tens and units parts, and the products of the parts are then calculated explicitly in a relatively simple multiplication-only stage, before these contributions are then totalled to give the final answer in a separate addition stage.
Both are unsatisfied ; Buffy is ashamed of her dark desires, while Spike obsessively craves the love, trust, and affection that she is unwilling to give.
Both books give an impression of how food was prepared and served in the noble classes of England at that time.
Both Rhee and Kim Il Sung wanted to unite the Korean peninsula under their respective governments, but the United States refused to give South Korea any heavy weapons to ensure that its military could only be used for self-defense and preserving internal order.
Both give the misleading impression that he was younger than King Richard: he was at least several years older.
Both types of abnormalities can occur in gametes and therefore will be present in all cells of an affected person's body, or they can occur during mitosis and give rise to a genetic mosaic individual who has some normal and some abnormal cells.
Both continued to give speeches plugging the event.
Both Xenophon ( Cyropaedia, 7. 5. 28-30 ) and Herodotus ( The Histories, 1. 191 ) recount the fall of Babylon to Cyrus the Great, yet neither of these writers give the name of the king of Babylon.
Both animation fans and the UCLA Film and Television Archive have worked to give the classic Fleischer cartoons the credit they deserve, and high-quality restored editions of the Fleischer cartoons have also been made available on pay-cable, home video and DVD.
Both these literary figures, in the context of the broader contributions of Greek philosophy in the Classical and Hellenistic eras, were to give rise to idea of Political Science, the study of political evolution and the critique of governmental systems.

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