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Page "Arithmetical hierarchy" ¶ 26
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Note and while
Note, however, that currying, while similar, is not the same operation as partial function application.
Note: Step ( in the description below ) is defined as: a transfer / change of weight to the opposite foot while hopping ( this is usually minimal ; almost more of a scoot than a literal hop ).
Note that this brain-in-a-vat argument conflates cyberspace with reality, while the more common descriptions of cyberspace contrast it with the " real world ".
Note that while the terms demon and demonic are used in monotheistic faiths as antonyms to divine, they are in fact derived from the Greek word daimón ( δαίμων ), which itself translates as divinity.
( Note: On most location-based television shows, there will be two Assistant Location Managers that alternate episodes, allowing one to prep an upcoming episode while the other is on-set with the current one.
Note also that until well into the 20th Century, rather than an official readying the ball for scrimmage, the side entitled to the snap had complete custody of the ball and could snap it from the required spot at any time ; for instance, a tackled ball carrier might feign injury, then suddenly snap the ball while recumbent, there being no stance requirement yet.
Note also that ' br ' is an empty element in that, while it may have attributes, it can take no content and it may not have an end tag.
Methods PUT and DELETE are defined to be idempotent, meaning that multiple identical requests should have the same effect as a single request ( Note that idempotence refers to the state of the system after the request has completed, so while the action the server takes ( e. g. deleting a record ) or the response code it returns may be different on subsequent requests, the system state will be the same every time ).
Note that is positive while is negative ; in any reversible work-extracting process, entropy is overall not increased, but rather is moved from a hot ( high-entropy ) system to a cold ( low-entropy one ), decreasing the entropy of the heat source and increasing that of the heat sink.
Note that during the sort, the largest element is at the root of the heap at a, while at the end of the sort, the largest element is in a.
Note that the bilinearity and alternating properties imply anticommutativity, i. e., for all elements x, y in, while anticommutativity only implies the alternating property if the field's characteristic is not 2.
Note that while such perfect price discrimination is still a theoretical construct, it is becoming increasingly real with advances of information technology and micromarketing.
( Note that while Mercury does allow impure functionality, it is not necessary in most software, and serves primarily as a way of calling foreign language code.
Note that while the associations indicated between the concepts in each item in that list is very strong, it is not absolute.
Note that some of these tasks have direct real-world applications, while others more commonly serve as subtasks that are used to aid in solving larger tasks.
Note that that while bound orbits around a point mass or around a spherical body with an Newtonian gravitational field are closed ellipses, which repeat the same path exactly and indefinitely, any non-spherical or non-Newtonian effects ( as caused, for example, by the slight oblateness of the Earth, or by relativistic effects, changing the gravitational field's behavior with distance ) will cause the orbit's shape to depart from the closed ellipses characteristic of Newtonian two-body motion.
Note: while the 741 was historically used in audio and other sensitive equipment, such use is now rare because of the improved noise performance of more modern op-amps.
Note the intersection of the two circles — the distinction between short a, i and u is made by both speakers, but Arabic lacks the mid articulation of short vowels, while Hebrew lacks the distinction of vowel length.
( Note: Astronomy should not be confused with astrology, which assumes that people's destiny and human affairs in general are correlated to the apparent positions of astronomical objects in the sky -- although the two fields share a common origin, they are quite different ; astronomers embrace the scientific method, while astrologers do not.
Note that only the step of substrate unfolding requires energy from ATP hydrolysis, while ATP-binding alone can support all the other steps required for protein degradation ( e. g., complex assembly, gate opening, translocation, and proteolysis ).
Note that while Nashville received only 26 % of the votes and was significantly behind Memphis in the first round, it won the election by winning the second round.
( Note that six of the squares only share vertices with the triangles while the other twelve share an edge.
Note that while most compilers will not output a binary given a compile-time error some do ;
Note that the power injected by the torque depends only on the instantaneous angular speed – not on whether the angular speed increases, decreases, or remains constant while the torque is being applied ( this is equivalent to the linear case where the power injected by a force depends only on the instantaneous speed – not on the resulting acceleration, if any ).
Note that the flatter-bottomed karahi ( right ) is sitting on an ordinary burner cover, while the round-bottomed wok is balanced on a wok-ring

Note and both
Note however that both in algebra and model theory the binary operations considered are defined on all of S × S.
Note that this statement is only true when the refractive indices of both materials are real numbers, as is the case for materials like air and glass.
* Note: Contains both the original version ( Japanese audio with English subtitles only ) and the edited G version ( English audio only ).
* Note: Contains both the Japanese version and uncut English dub and audio commentary with Steve Ryfle and Stuart Galbraith IV.
Note: The above definition of group velocity is only useful for wavepackets, which is a pulse that is localized in both real space and frequency space.
) Note that not all airports are assigned codes in both systems — for example, airports that do not have airline service may not need an IATA code.
To this plan both Britain and France gave a general assent, and the Andrássy Note was adopted as the basis of negotiations.
Note that there is no contradiction among these two results ; both computations are correct.
Note that from the perspective of the smaller-mass object — from the moon, in the preceding example — a spacecraft might appear to orbit in an irregular path about the or point, but from the perspective above the orbital plane, it becomes clear that both the smaller mass and the spacecraft are orbiting the larger mass ( or more precisely, all of the objects are in orbit around the barycenter of the system ); they simply have overlapping orbital paths.
Note: the president is both the chief of state and head of government
On April 23, 1998, the Ministry of Foreign Affairs of the Republic of the Marshall Islands issued an official Circular Note, denouncing representatives of both " EnenKio " and " Melchizedek " for making fraudulent representations.
Note the coats of arms both bear on their clothing — Malcolm wears the Lion of Scotland, which historically was not used until the time of his great-grandson William I of Scotland | William the Lion ; Margaret wears the supposed arms of Edward the Confessor, her grand-uncle, although the arms were in fact concocted in the later Middle Ages.
( Note that in both of those examples those quantities would be maximized rather than minimized ).
( Note: Lava flows refer to both actively flowing lava and the solidified landforms they produce.
Note that both " persons and estates " are to be protected from the arbitrary power of any magistrate, inclusive of the " power and will of a legislator.
Note that in both three-and four-level lasers, the energy of the pumping transition is greater than that of the laser transition.
Note that an enzyme that displays both PLA1 and PLA2 activities is called a Phospholipase B.
Note that both arrows point in the same direction.
Note that the letter ' h ' in both the transcription and transliteration forms should logically be omitted.
Note that only two sequences of moves by O ( both starting with center, top-right, left-mid ) lead to a draw, with the remaining sequences leading to wins from X.
Note that in this equation, both force and displacement are vector quantities.
Note that both the limit and the colimit functors are covariant functors.
Note that the weighted ski is on-edge and forming an arc ; if both legs were parallel the skis would begin to smoothly carve.
Note 2: A data transmission circuit may transfer information in ( a ) one direction only, ( b ) either direction but one way at a time, or ( c ) both directions simultaneously.

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