Important results include the Bolzano – Weierstrass and Heine – Borel theorems, the intermediate value theorem and mean value theorem, the fundamental theorem of calculus, and the monotone convergence theorem.

; Important results

Important results in complexity theory allow us to relate this complexity class with other classes, telling us about the relative power of the resources involved.

Important results of Itō calculus include the integration by parts formula and Itō's lemma, which is a change of variables formula.

Important links have been made between world-class, championship individual and team sports performance and business results.

Important results on this type of zero of an L-function were obtained in the 1930s by Carl Ludwig Siegel, from whom they take their name ( he was not the first to consider them, and they are sometimes called Landau-Siegel zeroes to acknowledge also the work of Edmund Landau ).

Important numberings are the Gödel numbering of the terms in first-order predicate calculus and numberings of the set of computable functions which can be used to apply results of computability theory on the set of computable functions itself.

Important irrigated crops include barley, corn, cotton, various fruits, grapes, opium poppies, sugar beets, roses, and tobacco.

Important cities along the coast include Batumi, Burgas, Constanța, Giresun, Hopa, Istanbul, Kerch, Mangalia, Năvodari, Novorossiysk, Odessa, Ordu, Poti, Rize, Samsun, Sevastopol, Sochi, Sukhumi, Trabzon, Varna, Yalta and Zonguldak.

Important sub-disciplines within bioinformatics and computational biology include:

Important constraints to economic development include the CAR's landlocked position, a poor transportation system, a largely unskilled work force, and a legacy of misdirected macroeconomic policies.

Important areas of study include chemical thermodynamics, chemical kinetics, electrochemistry, quantum chemistry, statistical mechanics, and spectroscopy.

Important organocarbonates include dimethyl carbonate, the cyclic compounds ethylene carbonate and propylene carbonate, and the phosgene replacement, triphosgene.

Important areas of study include chemical thermodynamics, chemical kinetics, electrochemistry, statistical mechanics, spectroscopy, and more recently, astrochemistry.

Important manufacturing centres in the region include Pictou County, Truro, the Annapolis Valley and the South Shore, and the Strait of Canso area in Nova Scotia, as well as Summerside in Prince Edward Island, and the Miramichi area, the North Shore and the upper Saint John River valley of New Brunswick.

Important types include:

Important vegetables include tomato, aubergine ( eggplant ), potato, green beans, okra, green peppers, and onions.

Important topics addressed in these letters include ecclesiology, the sacraments, and the role of bishops.

Important Gujarati Muslim communities in the city include the Memon, Chhipa, Ghanchi, Khoja, Bohra and Tai.

Important works from the 100s include the Attic Nights of Aulus Gellius, a collection of anecdotes and reports of literary discussions among his friends ; and the letters of the orator Marcus Cornelius Fronto to Marcus Aurelius.

Important examples include the mica, chlorite, and the kaolinite-serpentine groups.

Important bilateral donors include Canada, Denmark, Germany, Ireland, Iceland, Japan, the Netherlands, Norway, Sweden, Republic of China ( Taiwan ), the United Kingdom, and the United States.

Important philosophers of mind include Plato, Descartes, Leibniz, Kant, Martin Heidegger, John Searle, Daniel Dennett and many others.

Important properties that various operators may exhibit include linearity, continuity, and boundedness.

Important naval victories of the Ottoman Empire in this period include the Battle of Preveza ( 1538 ); Battle of Ponza ( 1552 ); Battle of Djerba ( 1560 ); conquest of Algiers ( in 1516 and 1529 ) and Tunis ( in 1534 and 1574 ) from Spain ; conquest of Rhodes ( 1522 ) and Tripoli ( 1551 ) from the Knights of St. John ; capture of Nice ( 1543 ) from the Holy Roman Empire ; capture of Corsica ( 1553 ) from the Republic of Genoa ; capture of the Balearic Islands ( 1558 ) from Spain ; capture of Aden ( 1548 ), Muscat ( 1552 ) and Aceh ( 1565 – 67 ) from Portugal during the Indian Ocean expeditions ; among others.

Important and commonly encountered probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution.

Important widely recognized types of property include real property ( the combination of land and any improvements to or on the land ), personal property ( physical possessions belonging to a person ), private property ( property owned by legal persons or business entities ), public property ( state owned or publicly owned and available possessions ) and intellectual property ( exclusive rights over artistic creations, inventions, etc.

Important punk zines include Maximum RocknRoll, Punk Planet, No Cure, Cometbus, Flipside, and Search & Destroy.

Important themes include:

Important Alien civilisations include the Puppeteers, paranoid pacifist herbivore centaurs, and the Kzinti, carnivorous warlike felines, who fought multiple wars over hundreds of years against the Humans, being defeated each time.

Important potential properties of statistics include completeness, consistency, sufficiency, unbiasedness, minimum mean square error, low variance, robustness, and computational convenience.

Important evidence against the tabula rasa model of the mind comes from Behavioural genetics, especially twin and adoption studies.

Important new evidence on a plausible mechanism for the evolution of " gay genes " has emerged from the work of Camperio-Ciani.

Important evidence for the Big Bang was discovered at another Bell Labs facility in Holmdel by Arno Penzias and Robert Wilson, both of whom won the Nobel Prize in Physics for their work here.

Important evidence to analyze when doing network forensics of a suspected SSL MITM attack include:

Important evidence was neither exploited nor preserved.

* Important archaeological sites in the vicinity of Naqadeh include Teppe Hasanlu, northwest of Naqadeh and famous for its " Golden Cup ", and Hajji Firuz Tepe where some of the oldest evidence for winemaking has been uncovered.

Important teeth for carnivorans are the large, slightly recurved canines, used to dispatch prey, and the carnassial complex, used to rend meat from bone and slice it into digestible pieces.

Important from this period are six sonate a quattro, or string sonatas, composed in three days, unusually scored for two violins, cello and double bass.

Important also is De viris illustribus, written at Bethlehem in 392, the title and arrangement of which are borrowed from Suetonius.

Important human migrations occurred in the Pacific in prehistoric times, most notably those of the Polynesians from the Asian edge of the ocean to Tahiti, Hawaii, New Zealand, Easter Island and possibly even America.

Important philosophical problems derive from the epistemology of perception — how we can gain knowledge via perception-such as the question of the nature of qualia.

Important historical study of Cubism began in the late 1920s, drawing at first from sources of limited data, namely the opinions of Guillaume Apollinaire.

H. Bruce Franklin ’ s most recent book, The Most Important Fish in the Sea: Menhaden and America is an interdisciplinary study of the role of menhaden in American environmental, economic, social, political, and cultural history from the seventeenth into the twenty-first centuries.

Important lakes, aside from Alaotra, include Lake Kinkony in the northwest and Lake Ihotry in the southwest.

In 1999 Time named Pankhurst as one of the 100 Most Important People of the 20th Century, stating: " she shaped an idea of women for our time ; she shook society into a new pattern from which there could be no going back.

Important details of his biography are gleaned from the works of the 1st century CE Roman-Jewish historian Josephus Flavius.

Important support for his work also came from Walter Ramsden Fawkes, of Farnley Hall, near Otley in Yorkshire, who became a close friend of the artist.

Important members of the party have included Minneapolis mayor Hubert H. Humphrey and Minnesota Attorney General Walter Mondale, who each went on to be United States Senators, Vice Presidents of the United States, and unsuccessful Democratic nominees for president, Humphrey in 1968 and Mondale in 1984 ; Eugene McCarthy, a Senator who ran for the Democratic presidential nomination in 1968 as an anti-Vietnam War candidate ; and Paul Wellstone, a Senator from 1991 – 2002 who became an icon of populist progressivism.

Important poems from her last years include " Mondesaufgang " (" Moonrise "), " Durchwachte Nacht " (" Sleepless Night ") and " Im Grase " (" In the Grass ").

Important national interests include, for example, regions in which we have a sizable economic stake or commitments to allies, protecting the global environment from severe harm, and crises with a potential to generate substantial and highly destabilizing refugee flows.

* Algae: The World's Most Important " Plants " video lecture by Russell Chapman from 2006.

Important examples of linear operators include the derivative considered as a differential operator, and many constructed from it, such as del and the Laplacian.