However, the proofs are not exactly equivalent.

However, in projective geometry every conic section is equivalent to an ellipse.

However, should a solution be equivalent to its own 90 degree rotation ( as happens to one solution with five queens on a 5x5 board ) that fundamental solution will have only two variants ( itself and its reflection ).

However, the English one underwent a great upward mobility during the Middle Ages, becoming associated with the aristocracy, while its German equivalent retained the humble meaning of " servant ".

However, the verb " attend " in English is translated as assister in French and asistir in Spanish, both of which could be further misinterpreted as equivalent to the English " assist ", which means " to help " ( which is also another meaning of the Spanish's asistir ).

However the situation is different when the language is of arbitrary large cardinality since then, though the completeness and compactness theorems remain provably equivalent to each other in ZF, they are also provably equivalent to a weak form of the axiom of choice known as the ultrafilter lemma.

However, for identical 8-bit ( or lower ) image data, PNG files are typically smaller than the equivalent GIFs, due to the more efficient compression techniques used in PNG encoding.

However, it is an empirical fact that microscopic particles of the same species have completely equivalent physical properties.

However, except for a few sheltered inland valleys during December and January, precipitation in Japan is above of rainfall equivalent in all months of the year, and in the wettest coastal areas it is above per month throughout the year.

However, more expressive languages are likely to require more complex logic and algorithms to construct equivalent inferences.

However, after a process of assessment by the provincial regulatory bodies, registrants are all simply known as ' midwives ', ' registered midwives ' or by the French-language equivalent, ' sage femme ', regardless of their route of training.

However, the recently discovered language of Zialo has nasal equivalent for each of its seven vowels.

However a phoneme is generally regarded as an abstraction of a set ( or equivalence class ) of speech sounds ( phones ) which are perceived as equivalent to each other in a given language.

However, there is no exact equivalent of a guilty plea in German criminal procedure.

However, it has been claimed that potato chips may actually contain less sodium / salt than the equivalent weight in corn flakes.

However the first result is for positive linear functionals, not bounded linear functionals, so the two facts are not equivalent.

However, additional issues are raised by the attested usage of the logically equivalent alternative constructions of this distributive expression, using:

However, "" should be transliterated as "" without the letter ' h ', which is found only in the English rendition of the name, the common equivalent of Greece since: → Ellas → Hellas ( in English renderings ).

However, this scenario can be resolved within the standard framework of special relativity ( because the twins are not equivalent ; the space twin experienced additional, asymmetrical acceleration when switching direction to return home ), and therefore is not a paradox in the sense of a logical contradiction.

However, by rotating the board, we will find that in the first turn, every corner mark is strategically equivalent to every other corner mark.

However, not all disabled sports are adapted ; several sports that have been specifically created for persons with a disability have no equivalent in able-bodied sports.

However, it is the interpolation method that in theory exactly reconstructs any given bandlimited x ( t ) with any bandlimit B < 1 /( 2T ); any other method that does so is formally equivalent to it.

However, some significant differences between neoplatonism and Gregory's thought exist, such as Gregory's statement that beauty and goodness are equivalent, which contrasts with Plotinus ' view that they are two different qualities.

However, to supply the same amount of power, the current must be greater than an equivalent 115 V or 230 V circuit ; greater current requires larger conductors or more energy lost as heat.

However, as a practicing historian, he, himself, has left few clues to the amount of professional scholarship that he used when writing history.

However, as witnessed by the large corporate bond calendar at present, as well as the record amount of municipal bond issues approved by voters, the over-all demands for capital funds seem likely to remain high, so that any downward pressure on rates from reduced demand should not be great.

However, some systems have a maximum amount of energy that they can hold, and as they approach that maximum energy their entropy actually begins to decrease.

However, the Vandals loot a great amount of treasure.

However, slow phosphor has the negative side-effect of causing image smearing and blurring when there is a large amount of rapid on-screen motion occurring.

However, there are cases in which the eyes of an albinistic person appear red or purple, depending on the amount of pigment present, due to the red of retina being visible through the iris.

However, there was still £ 13, 000 to pay on a mortgage, a fairly large amount of money in the 1880s, and Henry was at the time still only a mere parish priest.

However, at puberty, female sex hormones, mainly estrogen, promote breast development, which does not occur in men, due to the higher amount of testosterone.

However, unless the airflow is adjusted as well, the flame temperature will decrease because an increased amount of gas is now mixed with the same amount of air, starving the flame of oxygen.

However, the casino may only pay 4 times the amount wagered for a winning wager.

" However, coercion does not necessarily amount to destruction.

However, because fiat money is backed by government guarantee of a certain amount of goods and services, where the value of this is in turn determined by free market currency exchange rates, similar to the case for the international market exchange values which determines the value of metals which back commodity money, in practice there is very little economic difference between the two types of money ( types of currencies ).

However, it is finding a significant amount of success in schools because of the inherent differences: student voice is central to the daily schooling experience because students spend all day there.

However practical devices have a limit to the peak current they can pass, and the pulse must therefore be widened, to around 120 degrees, to obtain a reasonable amount of power, and the efficiency is then 60-70 %.

However, if the shape is complex with many features, the algorithm spends a large amount of time tracing the edges of the region trying to ensure that all can be painted.

However, since the Earth reflects about 30 % of the incoming sunlight, the planet's effective temperature ( the temperature of a blackbody that would emit the same amount of radiation ) is about − 18 ° C, about 33 ° C below the actual surface temperature of about 14 ° C.

However, many of the minor substances in honey can be affected greatly by heating, changing the flavor, aroma, or other properties, so heating is usually done at the lowest temperature possible for the shortest amount of time.

However, if the vehicle travels for a certain amount of time at a speed x and then the same amount of time at a speed y, then its average speed is the arithmetic mean of x and y, which in the above example is 50 kilometres per hour.

However the Hohmann transfer takes an amount of time similar to ½ of the orbital period of the outer orbit, so in the case of the outer planets this is many years – too long to wait.

However, there has been no small amount of inconsistency in the usage of the " is-a " link: Ronald J. Brachman wrote a paper titled " What IS-A is and isn't ", wherein 29 different semantics were found in projects whose knowledge representation schemes involved an " is-a " link.

However, the Financial Action Task Force on Money Laundering ( FATF ), an intergovernmental body set up to combat money laundering, stated that " overall it is absolutely impossible to produce a reliable estimate of the amount of money laundered and therefore the FATF does not publish any figures in this regard ".

However, there is a certain amount of design philosophy similarity ( e. g., considerable orthogonality and flexible addressing modes ), some assembly language syntax resemblance, as well as opcode mnemonic similarity, but the 6809 is a derivative of the 6800 whereas the 68000 was a totally new design.

However, it proved costly to keep, consumed a vast amount of money and subsequently led to other parts of the French Armed Forces being underfunded.