Although counting the number of elements in a set is a rather broad mathematical problem, many of the problems that arise in applications have a relatively simple combinatorial description.

Although the metre is now defined as the path length travelled by light in a given time, the practical laboratory length measurements in metres are determined by counting the number of wavelengths of laser light of one of the standard types that fit into the length, and converting the selected unit of wavelength to metres.

Although it's possible to augment simple reference counts in a variety of ways, often a better solution can be found by performing reference counting in a fundamentally different way.

Although the Samaritans stopped counting for the Jubilee some hundreds of years ago, according to a recent report an effort is underway to determine the date when counting ceased in order to resume.

Although the NORC study was not primarily intended as a determination of which candidate " really won ", analysis of the results, given the hand counting of machine-uncountable ballots due to various types of voter error, indicated that they would lead to differing results, reported in the newspapers which funded the recount, such as The Miami Herald ( The Miami Herald Report: Democracy Held Hostage ) or the Washington Post.

" Although he clarified his statement as merely a poor choice of words, critics of Diebold and / or the Republican party interpreted this as at minimum an indication of a conflict of interest, at worst implying a risk to the fair counting of ballots.

Although the language is long extinct it is arguable that traces of its vocabulary persisted into the modern era in the form of " counting scores " and in a handful of dialectal words.

Although the number of registrations has topped 100, 000, a design flaw in the counting process means that it counts users who abandoned the signup process mid way ; the actual number of posters is smaller, clocking in at around 38, 700 as of October 2008.

Although it is a crossover film, it is primarily a Rugrats movie as the main plot focuses on those characters, and the characters from The Wild Thornberrys are supporting characters, not counting Nigel Thornberry ( voiced by Tim Curry ) who is in fact a main character.

* Vote-rigging: Although the counting at the local ballot boxes was conducted in public, with the ballot papers held up and the scores marked on boards, it was at the later stages where irregularities were frequently reported.

" Although Caesar says " at night " he specifically does not say " sunset " so we do not know how much the Gauls differed from others in methods of counting from midnight.

Although consistency in counting customers is probably more important than formulating a precise definition, a definition is needed nonetheless.

Although these sets certainly describe different things, they have the same counting sequence, namely the Catalan numbers.

Although this switch from counting rods to the abacus allowed for reduced computation times, it may have also led to the stagnation and decline of Chinese mathematics.

Although, for the United Kingdom, it was released on the same day, with both Part I and Part II counting as the song release.

Although the Codex Belli itself doesn't specify any rules for counting hits, two variants have become widely accepted at German events.

Although decimal up to 10, in most dialects the scheme then changes to counting in ( sub -) base 5.

Although not used as counting device, many Jews touch the knots on the tzitzits attached to their tallit ( prayer shawl ) at specific points in their prayers.

Although there is no question but that the process of washing fabrics involves a number of phenomena which are related together in an extremely complicated way and that these phenomena and their interrelations are not well understood at the present, this section attempts to present briefly an up-to-date picture of the physical chemistry of washing either fabrics or hard surfaces.

Although the matter has not been unequivocally demonstrated, the available data show that micelles in themselves do not contribute significantly to the detergency process.

Although the pause in the advance of general business activity this year has thus far been quite modest, it is hard to escape the conclusion that the softening process will continue into the first quarter of 1961 and possibly somewhat longer.

Although slab stock appeared first, it soon became apparent that for the production of cushions with irregular shapes, crowned contours, or rounded edges, the cutting of slab stock is a wasteful and uneconomical process.

' Although members are asked to confess serious sins to him, unlike the Roman Catholic Church, he is not the instrument of divine forgiveness, merely a guide through the repentance process ( and a judge in case transgressions warrant excommunication or other official discipline ).

Although the process of fermentation was not fully understood until Pasteur's work in 1857, it is still the first use of biotechnology to convert a food source into another form.

" Although many evangelicals allow that conversion can be a process, generally they see it as a specific, identifiable moment of time when a person simply and sincerely trusts in Jesus Christ as savior.

Although some of Chaplin's critics have claimed that credit for his film music should be given to the composers who worked with him, for example Raksin, who worked with Chaplin on Modern Times, has stressed Chaplin's creative position and active participation in the composing process.

Although the FARC and ELN accepted participation in the peace process, they did not make explicit commitments to end the conflict.

Although many Canadian whiskies are still labelled as “ rye ”, the modern mash bill for a Canadian “ rye ” whisky often contains little or no rye grain, and their flavour is derived in other ways ( such as flavour development from the aging process, blending with stronger-tasting Canadian whiskies, and the addition of flavourings ).

Although modern steel outperforms these swords, microscopic chemical reactions in the production process may have made the blades extraordinary for their time.

Although deprogrammers prepare families for the process, exit counselors tend to work more closely with families and expect them to contribute more to the process ; that is, exit counseling requires that families establish a reasonable and respectful level of communication with their loved one before the exit counseling proper can begin.

Although not much is known about the original process, it is assumed that Leichleitner emeralds were grown in acid conditions.

Although the parliamentary process had disappointed the labour movement, dominance in the Finnish Parliament and in legislation seemed to be the only true pathway to reach a more economically and socially balanced society.

Although saltpeter from new Prussian-style putrefaction works had not been produced yet ( the process taking about 18 months ), in only a year France had gunpowder to export.

Although the extraction process, using low-temperature gas liquefaction, was not developed in time to be significant during World War I, production continued.

Although the Sixth Amendment mandates the right to a jury trial in any criminal prosecution, the vast majority of criminal cases in the United States are resolved by the plea-bargaining process.

Although " icing " increases alcohol content, most of the United States breweries simply add water back into their beer after the icing process to bring the alcohol content back down to nearly the same levels.

Although by 1000 Germanic conquest of central, western, and southern Europe west of and including Italy was complete, excluding only Muslim Iberia, there was no process equivalent to Han sinification, and " Germany " remained largely a conceptual term referring to an amorphous area of central Europe.

Although some of his pieces sound similar to those written by minimalist composers, Adams actually rejects the idea of mechanistic procedure-based or process music ; what Adams took away from minimalism was tonality and / or modality, and the rhythmic energy from repetition.

Although kosher, the giraffe is not slaughtered today because the process would be very costly.

Although a process of media deregulation has placed the majority of the western broadcast media in private hands, there still exists a strong government presence, or even monopoly, in the broadcast media of many countries across the globe.

Although this process had been going on since the mid-17th-18th century, after 1948 it became official government policy and became known worldwide as apartheid.