Isetha

Izinketho, Ukusethwa Kwamakheli-Isakhiwo, Izinkinobho Zokuhlukanisa, Imifanekiso Ye-Venn

Isetha Uhlolojikelele

Isibalo, isethi iqoqo noma uhlu lwezinto.

Amasethi awagcini nje ngezinombolo, kodwa angaqukatha noma yini okubandakanya:

• ukudla esiqandisini sakho;
• amaplanethi ohlelweni lwelanga;

Ngisho noma amasethingi angaqukatha noma yini, ngokuvamile avame ukubhekisela ezinombeni ezihambisana nephethini noma ezihlobene ngandlela-thile njenge:

• iqoqo lezinombolo ngisho nezinombolo ezingaphansi kwezingu-10: (0, 2, 4, 6, 8);
• iqoqo lezinombolo ze-12: (1, 2, 3, 4, 6, 12).

Setha Ukwaziswa

Izinto ezisetiwe zibizwa ngokuthi izakhi futhi inothi noma imihlangano elandelayo isetshenziselwa amasethi:

• Amagama angama-single amasha asetshenziselwa ukukhomba amasethi - njengeJ, E, noma F ;
• Izincwadi ezincane noma izinombolo ezisetshenziselwa izakhi zethimba;
• Ama-braces angu-curly {} asho uhlu lwezinto ezisethiwe;
• Ama-Commas asetshenziselwa ukwehlukanisa izakhi ezibekiwe.

Ngakho-ke, izibonelo zokubeka isaziso kuzoba:

J = {jupiter, saturn, uranus, neptune}

E = {0, 2, 4, 6, 8};

F = {1, 2, 3, 4, 6, 12};

Ukuhlelwa kwe-Element nokuphindaphinda

Izinto ezisetiweni akudingeki ukuba zibe kunoma yikuphi ukuhleleka ngakho ukusetha J ngaphezulu kungabhalwa futhi ngokuthi:

J = {ukushisa, i-jupiter, i-neptune, i-uranus}

noma

J = {neptune, jupiter, uranus, saturn}

Izinto zokuphinda aziguquli isethi noma, ngakho:

J = {jupiter, saturn, uranus, neptune}

futhi

J = {jupiter, saturn, uranus, neptune, jupiter, saturn}

isethi efanayo ngoba zombili ziqukethe izakhi ezine kuphela: i-jupiter, i-saturn, i-uranus ne-neptune.

Isetha kanye ne-Ellipses

Uma kunezinombolo ezingenamkhawulo - ezingenamkhawulo - noma ezingenamkhawulo esethi, i-ellipsis (...) isetshenziselwa ukubonisa ukuthi iphethini yesethi iyaqhubeka kuze kube phakade kuleso siqondiso.

Isibonelo, iqoqo lezinombolo zemvelo liqala ngo-zero, kodwa lingapheli, ngakho-ke lingabhalwa ifomu:

{0, 1, 2, 3, 4, 5, ... }

Esinye isethi esikhethekile sezinombolo ezingapheli yisethi yezinombolo. Njengoba izinombolo zingase zenzeke noma zibi, noma kunjalo, isethi isebenzisa i-ellipses kokubili ekugcineni ukubonisa ukuthi isethi iqhubeka kuze kube phakade kuzo zonke izinkombandlela:

{ ... , -3, -2, -1, 0, 1, 2, 3, ... }

Olunye ukusetshenziswa lwe-ellipses ukugcwalisa phakathi kwesethi enkulu njengokuthi:

{0, 2, 4, 6, 8, ..., 94, 96, 98, 100}

I-ellipsis ibonisa ukuthi iphethini - ngisho nezinombolo kuphela - iqhubeka ngesigaba esingabhalwanga esethi.

Izisetho ezikhethekile

Amasethi akhethekile asetshenziselwa njalo abonakala ngokusebenzisa izinhlamvu ezithile noma izimpawu. Lokhu kufaka:

• Ø noma {} - isethi esingenalutho - isethi engenamakhi ;
• U - isethi yonke - isethi equkethe zonke izakhi ezihlobene nencazelo ethize ethile ;
• Z - isethi yazo zonke izinombolo: Z = { ... , -3, -2, -1, 0, 1, 2, 3, ... };
• N - izinombolo zemvelo (izinombolo eziqondile): N = {0, 1, 2, 3, 4, 5, ... }.

Inkambo vs. Izindlela Ezichazayo

Ukubhala noma ukubeka uhlu lwezinto ezisetshenziselwe isethi, njengeqoqo lamaplanethi angaphakathi noma asezweni elisesimweni sethu sobusuku, libhekwa njengokuthi i- roster notation noma indlela ye-roster .

T = {mercury, venus, umhlaba, mars}

Enye indlela yokukhomba izakhi zesethi usebenzisa indlela echazayo, esebenzisa isitatimende esifushane noma igama ukuchaza isethi njengale:

T = {amaplanethi asemhlabeni}

I-Notation Yomakhi Wokusetha

Okunye okunye okusetshenziselwa ukuthi kusetshenziswe indlela kanye nezindlela ezichazayo ukusebenzisa isitifiketi sokwakha isakhi, okuyindlela encane echaza umthetho wokuthi izakhi zesethi zilandelwa (umthetho owenza amalungu abekwe eceleni) .

Ukukwazisa okwakha isakhi seqoqo lezinombolo zemvelo kunkulu kune-zero yi:

{x | x ∈ N, x > 0 }

noma

{x: x ∈ N, x > 0 }

Ekwazisweni kwe-set-builder, incwadi "x" iyinhlangano eguquguqukayo noma indawo yokuhlala, engashintshwa nanoma iyiphi enye incwadi.

Shorthand Characters

Izinhlamvu ezincane ezisetshenziselwa ukukwazisa okwakha isethi zifaka:

• Ibha eliqondile noma ikholoni ( | noma : izinhlamvu) - abahlukanisi bafundwa njengaleyo;
• I-epsilon engezansi ( ∈ umlingiswa) - ifundwa njengengxenye ye;
• Uhlamvu lwe-- - lufundwa njengelona isici.

Ngakho, {x | x ∈ N, x > 0 } izofundwa njenge:

"Iqoqo lakho konke x , okufana nokuthi x iyisici seqoqo lezinombolo zemvelo futhi x lingaphezulu kuka-0."

Isetha kanye nemifanekiso ye-Venn

Umdwebo we-Venn - ngezinye izikhathi obizwa ngokuthi umdwebo osetshenzisiwe - usetshenziselwa ukukhombisa ubudlelwane phakathi kwezici zamasethi ahlukene.

Esikhathini esingenhla, isigaba esiqhamukayo somdwebo weVenn sibonisa ukuhlangana kwamasethingi e-E no-F (izakhi ezivame kokubili isethi).

Ngaphansi kwalokhu kubhalwe isaziso se-set-builder for the operation (i-downside down "U" isho ukuhlukanisa):

E ∩ F = {x | x ∈ E , x ∈ F}

Umngcele we-rectangular kanye no-U ekhoneni lomdwebo we-Venn ubonisa isethi yonke yezinto ezicatshangelwe kulo msebenzi:

U = {0, 1, 2, 3, 4, 6, 8, 12}