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, his astronomical clock and rotating armillary sphere still relied on the use of flowing water ( i. e. hydraulics ), while European clockworks of the following centuries shed this old method for a more efficient driving power of weights, in addition to the escapement mechanism.

However with the help of the correct atomic weights for copper and oxygen ( which Dalton did not know ), it is determined that the formulas of these two oxides are Cu < sub > 2 </ sub > O and CuO.

However, in his laboratory notebook under the date 6 September 1803 there appears a list in which he sets out the relative weights of the atoms of a number of elements, derived from analysis of water, ammonia, carbon dioxide, etc.

However, Crawford later accused Davis of kicking her during the filming of one scene in which Jane attacks Blanche ; Crawford reportedly retaliated by wearing weights under her clothes during a scene in which Davis had to carry her.

( However, as cost-benefit analysis may also assign different social welfare weights to different individuals, e. g. more to the poor, the compensation criterion is not always invoked by cost-benefit analysis.

However, the most popular weights for AEGs ( automatic electric guns ) and GBB * ( Gas Blow back guns ) are 0. 20g and 0. 25g (* These weights are generally specified for pistols whose FPS is approx.

However, she is a well intentioned character, a loving wife and mother, who tries to comfort her husband by suggesting he removes his handicap weights.

However, it has two graph-theoretic interpretations: as the sum of weights of cycle covers of a directed graph, and as the sum of weights of perfect matchings in a bipartite graph.

However, the notion of isomorphism may be applied to all other variants of the notion of graph, by adding the requirements to preserve the corresponding additional elements of structure: arc directions, edge weights, etc., with the following exception.

However, as trains, cars and locomotives began to get heavier and larger, the Lackawanna needed to build a new bridge across the river to support the heavier weights.

However, more careful measurements of the atomic weights, such as those compiled by Jöns Jakob Berzelius in 1828 or Edward Turner in 1832, disproved the hypothesis.

However, even in lighter weights, some letters do not look consistent.

However tankage and pump weights are high due to insulation and low propellant density ; and this wipes out much of the advantage.

However their weights and alloys have been changed for easy identification purposes.

However, many references in 15th century sources to portable clocks ' without weights ', and at least two surviving examples, show that spring driven clocks existed by the early years of that century.

) However, weights show tremendous seasonal variation.

However, one gram of hydrogen reacts with 8 grams of oxygen to give water or with 35. 5 grams of chlorine to give hydrogen chloride: hence 8 grams of oxygen and 35. 5 grams of chlorine can be taken to be equivalent to one gram of hydrogen for the measurement of equivalent weights.

However, their natural denotations of weights and measures were superficially meaningless: " two minas, a shekel and two parts ".

However bullet types and weights are loaded that allow the. 25-06 to be used for taking game ranging from small animals like prairie dogs and coyotes to heavier elk.

However, Imperial weights and measures were most commonly used until the Commonwealth government began the metric changeover in the 1970s.

However, ambiguous wording in the 1864 Act meant that traders who possessed metric weights and measures were still liable to arrest under Act 5 and 6 William IV c63.