Podmnožica

Podmnožica X⊆Y v Eulerjevem diagramu

Podmnožica ali delna množica množice $Y$ je v matematiki množica $X$ , če so vsi elementi $X$ tudi v $Y$ . Relacijo z matematičnim zapisom zapišemo $X\subseteq Y$ . Ali drugače, $X\subseteq Y$ tedaj in le tedaj, ko $X$ ne vsebuje nobenega elementa, ki ni tudi član množice $Y$ . Množica $Y$ v tem primeru se imenuje supermnožica množice $X$ in zapišemo $Y\supseteq X$ .

Vsaka množica $Y$ je sama sebi podmnožica. Podmnožica $Y$ , ki ni enaka $Y$ , se imenuje prava. Če je $X$ prava podmnožica $Y$ , potem pišemo $X\subset Y$ .

X\subset Y

natanko tedaj, ko

X\subseteq Y\land X\neq Y

Različni zapisi

Pri zapisu podmnožic obstajata dva glavna načina. Starejši način uporablja znak $\subset$ za podmnožico in $\subseteq$ za pravo podmnožico. Novejši način uporablja znak $\subseteq$ za podmnožico in $\subset$ za pravo podmnožico. Wikipedija uporablja novejši način, ki ga zna zapisati večina spletnih brskalnikov.

Primeri

Množica {1, 2} je prava podmnožica {1, 2, 3}.

\{1,2\}\subset \{1,2,3\}

Množica {1, 2} je podmnožica sami sebi {1, 2}.

\{1,2\}\subseteq \{1,2\}

Množica naravnih števil N = {1, 2, 3, 4, 5, 6, ...} je prava podmnožica množice racionalnih števil Q.

\mathbb {N} =\{1,2,3,4,5,6,\dots \}\subset \mathbb {Q}

Množica P '₂₀₀₀ = {x : x je praštevilo > 2000} je podmnožica množice L '₁₀₀₀ = {x : x je liho število > 1000}

P_{2000}=\{x\mid x{\text{ je praštevilo}}>2000\}\subset L_{1000}=\{x\mid x{\text{ je liho število}}>1000\}

Vsaka množica A je po definiciji tudi podmnožica same sebe (A), ni pa vsaka tudi sama sebi prava.

A\subseteq A

Lastna množica A je poljubna podmnožica razen množice A same.

A\subset X,A\neq X

Prazna množica Ø = {} je prav tako podmnožica vsake poljubne množice X. To je zaradi tega, ker za prazno množico velja nepopolna definicija podmnožice X: ker prazna množica nima elementov, nujno vsebuje nič elementov, ki niso člani množice X. Tako je prazna množica vedno prava podmnožica razen sama sebi.

\emptyset \subseteq X

Read other articles:

Iklim sabana tropis

Zona iklim sabana tropis (Aw/As) di seluruh dunia . Iklim sabana tropis atau iklim tropis basah dan kering adalah jenis iklim tropis yang dicirikan dengan dua periode musim yang jelas, yakni musim penghujan dan musim kemarau serta cenderung memiliki tingkat curah hujan yang lebih rendah daripada iklim hutan hujan tropis dan iklim muson tropis. Selain itu, iklim sabana tropis merupakan jenis iklim tropis yang curah hujan di bulan terkeringnya kurang dari 60 mm (2,4 in) per bulan dan kurang dar...

Chittagong-10

Constituency of Bangladesh's Jatiya Sangsad Chittagong-10Constituencyfor the Jatiya SangsadDistrictChittagong DistrictDivisionChittagong DivisionElectorate469,314 (2018)[1]Current constituencyCreated1973Parliamentary PartyBangladesh Awami LeagueMember of ParliamentMd. Mohiuddin BacchuCity Council areaChattogram City CorporationPrev. ConstituencyChittagong-9 (Constituency 286)Next ConstituencyChittagong-11 (Constituency 288) Chittagong-10 is a constituency represented in the Jatiya San...

She Says (Unwritten Law song)

For the Howie Day song, see She Says (Howie Day song). 2005 single by Unwritten LawShe SaysSingle by Unwritten Lawfrom the album Here's to the Mourning ReleasedSeptember 2005Recorded2004 at Ocean Recording, Glenwood Place, and Royaltone in Burbank, The Blue Room in Laurel Canyon, Pulse in Hollywood, and Sound Wherehouse in Sherman OaksGenreAlternative rockLabelLavaSongwriter(s)Scott Russo, Aimee Allen, Phil JamiesonProducer(s)Sean BeavanUnwritten Law singles chronology Save Me (Wake Up Call) ...

Clean with Passion for Now

Clean with Passion for NowPoster promosiJudul asli일단 뜨겁게 청소하라 GenreKomedi romantisBerdasarkanClean with Passion for Nowoleh AaengoDitulis olehHan Hee-jungSutradaraNo Jong-chanPemeranKim Yoo-jungYoon Kyun-sangSong Jae-rimNegara asalKorea SelatanBahasa asliKoreaJmlh. episode16ProduksiProduser eksekutifKim Joo-seokPark Joon-seoRumah produksiDrama House [ko]The CollectiveDistributorJTBC Netflix (internasional)Rilis asliJaringanJTBCFormat gambar1080i (HDTV)Format au...

National Infantry Association

This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources.Find sources: National Infantry Association – news · newspapers · books · scholar · JSTOR (December 2022) National Infantry AssociationEstablishedApril 1982 (42 years ago) (1982-04)Headquarters3800 S Lumpkin Road, Columbus, GeorgiaCoordinates32°...

NGC 2527

Open cluster in the constellation Puppis NGC 2527Observation data (J2000 epoch)Right ascension08h 04m 58s[1]Declination−28° 08′ 48″[1]Distance1,960 ly (601 pc[2])Apparent magnitude (V)6.5 [1]Apparent dimensions (V)20'Physical characteristicsMass740[3] M☉Estimated age445 million years[2]810 million years[4]Other designationsNGC 2520, Cr 174AssociationsConstellationPuppisSee also...

Hongshuwan station

Metro station in Shenzhen, China Hongshuwan红树湾Chinese nameTraditional Chinese紅樹灣Simplified Chinese红树湾Literal meaningRed Tree BayTranscriptionsStandard MandarinHanyu PinyinHóngshù WānYue: CantoneseJyutpingHung4syu6 Waan1 General informationLocationNanshan District, Shenzhen, GuangdongChinaOperated bySZMC (Shenzhen Metro Group)Line(s) Line 2Platforms2 (1 island platform)Tracks2ConstructionStructure typeUndergroundAccessibleYesOther informat...

Новотитаровское сельское поселение

Сельское поселение России (МО 2-го уровня)Новотитаровское сельское поселение Флаг[d] Герб 45°14′09″ с. ш. 38°58′16″ в. д.HGЯO Страна Россия Субъект РФ Краснодарский край Район Динской Включает 4 населённых пункта Адм. центр Новотитаровская Глава сельского пос�...

B-300

Anti-tank weapon B-300 TypeAnti-tankPlace of originIsraelService historyUsed bySee OperatorsWarsLebanese Civil War1st and 2nd Intifada2006 Lebanon WarGaza War2020 Nagorno-Karabakh conflictProduction historyDesignerIsrael Military IndustriesDesigned1970sManufacturerIsrael Military IndustriesProduced1980s–presentSpecificationsMass3.65 kg (8.0 lb) empty 8 kg (18 lb) loaded [citation needed]Length1,440 mm (57 in)Crew1Caliber82 mm (3.2...

Holy Family (El Greco, Hospital de Tavera)

1595 painting by El Greco Holy FamilyArtistEl GrecoDimensions127 cm × 106 cm (50 in × 42 in)LocationHospital de Tavera, Toledo Holy Family is a 1595 oil on canvas painting by El Greco, painted during his time in Toledo and now in the Hospital de Tavera in that city. The work is very similar to those painted by the same artist during his stay in Rome. The artist frequently returned to the theme of the Holy Family. Though this work has similarities to...

Військово-музичне управління Збройних сил України

Військово-музичне управління Збройних сил України Тип військове формуванняЗасновано 1992Країна Україна Емблема управління Військово-музичне управління Збройних сил України — структурний підрозділ Генерального штабу Збройних сил України призначений для планува...

أرب 302

Arp 302 صورة Arp 302 مراقبة البيانات (حقبة حقبة) الكوكبة كوكبة العواء رمز الفهرس UGC 9618 (فهرس أوبسالا العام) المطلع المستقيم 14سا 56د 54ث الميل +24° 36.0′ 00″ الانزياح الأحمر 0.034505(10166 km/s) البعد 450 سنة ضوئية (150 فرسخ فلكي) نوع S+S الأبعاد الظاهرة 1′.6 (0′.6 × 0′.6 / 0′.9 × 0′.3) الق...

جنرال الجيش (رتبة عسكرية)

يفتقر محتوى هذه المقالة إلى الاستشهاد بمصادر. فضلاً، ساهم في تطوير هذه المقالة من خلال إضافة مصادر موثوق بها. أي معلومات غير موثقة يمكن التشكيك بها وإزالتها. (فبراير 2023) الرتب العسكرية المقارنة جنرال الجيش رتبة عسكرية، عادة ما يكون جنرال الجيش هو أعلى رتبة مستخدمة في وقت ال�...

Fossil fuel divestment

Removal of investment in companies involved in extracting fossil fuels to reduce climate change Not to be confused with Fossil fuel phase-out. As of 2021, 1,300 institutions possessing US$14.6 trillion have divested from the fossil fuel industry.[1] Fossil fuel divestment or fossil fuel divestment and investment in climate solutions is an attempt to reduce climate change by exerting social, political, and economic pressure for the institutional divestment of assets including stoc...

Malcolm Longair

British physicist Malcolm LongairCBE FRS FRSEMalcolm Longair in 2013 at the James Webb Space Telescope Advisory Committee (JSTAC), held at the Space Telescope Science Institute (STScI) in Baltimore. Portrait by Mark McCaughrean of the European Space AgencyBornMalcolm Sim Longair (1941-05-18) 18 May 1941 (age 83)[1]Dundee, ScotlandEducationMorgan AcademyAlma mater University of Dundee University of St Andrews University of Cambridge Spouse Deborah Howard &#...

Orange River

Major river in southern Africa For other uses, see Orange River (disambiguation). Orange RiverKai Garib (Groote Rivier), Gariep, Senqu, Oranje, Igqili( isiZulu and isiiXhosa)Sunset over the Orange River near Upington in the Northern CapeLocationCountryLesotho, South Africa, NamibiaDistrictMokhotlongDistrictThaba TsekaDistrictQacha's Nek, Quthing, Mohale's HoekPhysical characteristicsSourceMont-aux-Sources[1] • locationMaloti Mountains (Drakensberg), Lesotho &...

Ночная хоккейная лига

Не следует путать с Национальной хоккейной лигой (НХЛ). В статье не хватает ссылок на источники (см. рекомендации по поиску). Информация должна быть проверяема, иначе она может быть удалена. Вы можете отредактировать статью, добавив ссылки на авторитетные источники в виде ...

Akron, Ohio

Akron redirects here. For other uses, see Akron (disambiguation). City in Ohio, United StatesAkronCityDowntown AkronStan Hywet HallAkron Art MuseumCanal ParkGoodyear Airdock FlagSealLogoEtymology: from Ancient Greek ἄκρον (ákron) 'summit, high point'Nicknames: Rubber City, City of Invention, Rubber Capital of the World (historical)Interactive map of AkronAkronShow map of OhioAkronShow map of the United StatesCoordinates: 41°04′50″N 81°31′20″W / ...

Sean Mosley

American basketball player Sean MosleyMosley shooting for MarylandFree agentPositionShooting guardPersonal informationBorn (1989-03-19) March 19, 1989 (age 35)Baltimore, MarylandNationalityAmericanListed height6 ft 4 in (1.93 m)Listed weight210 lb (95 kg)Career informationHigh schoolSt. Frances Academy(Baltimore, Maryland)CollegeMaryland (2008–2012)NBA draft2012: undraftedPlaying career2012–presentCareer history2012–2013SKK Kotwica Kołobrzeg2014–2015Crai...

Taison

TaisonTaіson capitano allo Shakhtar nel 2019Nazionalità Brasile Altezza172[1] cm Peso68 kg Calcio RuoloAttaccante, ala Squadra PAOK CarrieraGiovanili 2001-2003 Brasil de Pelotas2004-2007 Internacional Squadre di club1 2007-2010 Internacional69 (9)[2]2010-2013 Metalist57 (13)2013-2021 Šachtar182 (37)2021-2022 Internacional42 (5)[3]2023- PAOK35 (3) Nazionale 2016-2018 Brasile8 (1) 1 I due numeri indicano le presenze e le re...