Sets

Elements, Set-Build-Notation, Zvigaro zveChina, Zviratidzo zveVenn

Inoisa Pfupiso

Mathematically, yakagadzirwa ndeyekuunganidza kana rutongwa rwezvinhu.

Setsiti haisi kungova nenhamba chete, asi inogona kuva nechinhu chipi zvacho chinosanganisira:

• zvokudya zviri mufiriji yako;
• mapurogiramu mune zvezuva;

Kunyange zvazvo mitsara inogona kuva nechinhu chero chipi zvacho, inowanzoreva nhamba dzinokodzera purogiramu kana dzakabatana mune imwe nzira dzakadai sa:

• chimiro chakanaka kunyange nhamba pasi pe10: (0, 2, 4, 6, 8);
• nheyo yezvikonzero zvehamba 12: (1, 2, 3, 4, 6, 12).

Isa Nyaya

Zvinhu zvakagadziriswa zvinonzi zvinhu uye zvinyorwa zvinotevera kana magungano zvinoshandiswa nemasethi:

• Tsamba dzisina kukodzera dzinoshandiswa kureva masero - akadai seJ, E, kana F ;
• Tsamba dzezasi dzepasi kana nhamba dzinoshandiswa kwezvinhu zvegadziriro;
• Curly braces {} kureva urongwa hwezvinhu zviri mumutsetse;
• Makomisheni anoshandiswa kuparadzanisa zvigadzirwa.

Saka, mienzaniso yekutarirwa kwaizove iyo:

J = {jupiter, saturn, uranus, neptune}

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

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

Element Order uye Kudzokorora

Zvinhu zvakagadziriswa hazvifanirwi kuva mune imwe nzira yakadaro kuitira kuti J setve kumusoro inogona kunyorwa se:

J = {kunyarara, jupiter, neptune, uranus}

kana

J = {neptune, jupiter, uranus, saturn}

Kudzokorora zvinhu hazvichinje zvakatemwa kana, zvekuti:

J = {jupiter, saturn, uranus, neptune}

and

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

iyo ndiyo yakagadzirirwa nokuti zvose zviri zviviri chete zvakasiyana-siyana: jupiter, saturn, uranus, uye neptune.

Sets and Ellipses

Kana pane chimiro chisingaverengeki -kana chechimiro chezvikamu mune imwe yakagadzirirwa, ellipsis (...) inoshandiswa kuratidza kuti chimiro chegadziriro chinoramba chiripo nekusingaperi mune izvozvi.

Semuenzaniso, sarudzo yemhando dzepanyama dzinotanga pa zero, asi haina mugumo, saka inogona kunyorwa nenzira iyo:

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

Imwe nharaunda yakakosha yenhamba isina mugumo ndeyeti yeti integers. Sezvo uwandu hunogona kuva hwakanaka kana husina kunaka, zvisinei, sarudzo inoshandisa ellipses kumativi ose maviri kuratidzira kuti zvakagadzirwa zvinoramba zvichienderera mberi mumativi ose maviri:

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

Imwe shanduro ye ellipses ndeyokuzadza pakati pegadziriro yakadai sa:

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

The ellipsis inoratidza kuti muenzaniso - kunyange nhamba chete - inopfuurira kuburikidza nechinyorwa chisina kunyorwa cheseti.

Masikirwo Akasiyana

Mitsara inokosha inoshandiswa kakawanda inoshandiswa uchishandisa tsamba chaiyo kana zviratidzo. Izvi zvinosanganisira:

• Ø kana {} - iyo isina chinhu - seti isina zvinyorwa ;
• U -i-universal set - seti rine zvinhu zvose zvine chokuita nechinangwa chairo chinotsanangurwa ;
• Z - nheyo yevose integers: Z = { ... , -3, -2, -1, 0, 1, 2, 3, ... };
• N - nhamba dzepanyama (positive integers): N = {0, 1, 2, 3, 4, 5, ... }.

Roster vs. Inotsanangura Nzira

Kunyora kunze kana kuverenga zvinyorwa zvegadziriro, zvakadai sekugadzirwa kwepurogiramu dzomukati kana dzenyika munzvimbo yedu yezuva, inotumidzwa sekunyorwa kwemazita kana nzira yekuita .

T = {mercury, venus, nyika, mars}

Imwe nzira yekutsanangurira zvikamu zvegadziriro iri kushandisa nzira inotsanangurwa, iyo inoshandisa mutauro mutsva kana zita kurondedzera zvakagadzirwa se:

T = {mapuraneti enyika)

Nheyo Yomugadziri Wakaisa

Imwe nzira yakasiyana nedzimwe nzira uye inotsanangura nzira yekushandisa yakagadzirirwa-kuvaka mucherechedzo , iyo inzira shorthand inotsanangura mutemo kuti zvinhu zvekutevedzwa zvinotevera (mutemo unoita kuti zvive nhengo dzeimwe yakagadzirirwa) .

Kuisa-kuvaka mucherechedzo wegadziriro yemhando dzepanyama huru kupfuura zero ndeye:

{x | x ∈ N, x > 0 }

kana

{x: x ∈ N, x > 0 }

Mukugadzirisa-kuvaka mucherechedzo, tsamba "x" inoshandiswa kana kuti inzvimbo, inogona kuchinjwa nemumwe tsamba.

Shorthand Characters

Shorthand mifananidzo inoshandiswa ne-set-builder notation inosanganisira:

• Rinovhara kana kuti coloni ( | kana : vateveri) - vaparadzi vanoverenga zvakadaro;
• The lowercase epsilon ( ∈ character) - inoverengwa sechinhu che;
• Iyo character - inoverengwa sechinhu che.

Saka, {x | x ∈ N, x > 0 } yaizoverengwa se:

"Iti yei yose x , yakadai kuti x chikamu chegadziro yemhando dzepanyama uye x inopfuura 0."

Sets and Venn Diagrams

Mufananidzo weVenn - dzimwe nguva unonzi semufananidzo wakaiswa - unoshandiswa kuratidza hukama pakati pezvinhu zvemaseri akasiyana.

Mumufananidzo wepamusoro, chikamu chinoputika chemufananidzo weVenn chinoratidza kupindirana kwemasero E uye F (zvinhu zvinowanikwa kune zvose zviri zviviri).

Pasi apa inorongedzwa seti-builder notation yebasa (iyo yakaderera pasi "U" inoreva kusangana kwepakati):

E ∩ F = {x | x ∈ E , x ∈ F}

Muganhu wakagadzikana uye tsamba U iri pakona yemufananidzo weVenn inomiririra wepasi rose yezvinhu zviri pasi pekufungisisa kwekushanda uku:

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