Izinto, i-Set-Build-Notation, i-Intersecting Sets, i-Venn Diagram
Ukusekela ngokubanzi
Imathematika, isethi yintlanganiso okanye uluhlu lwezinto.
Iisethi azihlanganisi nje ngamanani, kodwa zinokuqulatha nantoni na kuquka:
- ukutya kwifriji yakho;
- iiplanethi kwindlela yelanga;
Nangona iiseti zinokuthi ziqulethe nantoni na, zihlala zibhekisela kumanani afanelekileyo kumzekelo okanye axhamene ngandlela-thile njengaye:
- isethi sezinto ezintle namanani angaphantsi kwe-10: (0, 2, 4, 6, 8);
- isethi yezinto ezili-12: (1, 2, 3, 4, 6, 12).
Beka Ukwaziswa
Izinto ezisetiweyo zibizwa ngokuba yizinto kunye neenkcukacha ezilandelayo okanye iindibano zisetyenziswe ngeeseti:
- Iileta eziqhelekileyo ezingasetyenzisiweyo zisetyenziselwa ukuchonga isethi - njengeJ, E, okanye F ;
- Iileta ezincinci okanye iinombolo ezisetyenziselwa izinto zeetethi;
- Ubungqingili be-Curly {} bhekisela uluhlu lwezinto kwiisethi;
- Ii-Commas zisetyenziselwa ukwahlula izinto ezihleliweyo.
Ngoko, imizekelo yokumisela isethi yayiza kuba:
J = {jupiter, saturn, uranus, neptune}
E = {0, 2, 4, 6, 8};
F = {1, 2, 3, 4, 6, 12};
Umyalelo we-Element kunye nokuphindaphinda
Izinto ezenziwe kwisethi azimele zikho nawuphi na umyalelo ukwenzela ukuba isethi J apha ngasentla ingabhalwa njenge:
J = {i-saturn, jupiter, neptune, uranus}
okanye
J = {neptune, jupiter, uranus, saturn}
Izinto eziphindaphindayo ayitshintshi isethi okanye, oko kunjalo:
J = {jupiter, saturn, uranus, neptune}
kwaye
J = {jupiter, saturn, uranus, neptune, jupiter, saturn}
sisetyenzana esifanayo kuba zombini ziqukethe izinto ezine ezihlukeneyo: i-jupiter, i-saturn, uranus, kunye neptune.
Iisethi kunye nee-Ellipses
Ukuba kukho inani elingenamkhawulo - elingenamkhawulo-okanye elingenamkhawulo kwinqanaba, i-ellipsis (...) isetyenziselwa ukubonisa ukuba umzekelo wesethi uqhubeka ngonaphakade kwilo lathiso.
Ngokomzekelo, isethi yamanani asemvelo aqala kwi-zero, kodwa engapheli, ngoko ingabhalwa kwifomu:
{0, 1, 2, 3, 4, 5, ... }
Olunye uluhlu olukhethekileyo lweenombolo ezingapheliyo luhlu lweendidi. Ekubeni i-integers inokuthi ilungile okanye ayibi, nangona kunjalo, isethi isebenzisa i-ellipses kuzo zombini iziphelo ukubonisa ukuba isethi iyaqhubeka ngonaphakade kwiindlela ezimbini:
{ ... , -3, -2, -1, 0, 1, 2, 3, ... }
Olunye usetyenziso lwe-ellipses kukuzalisa phakathi kwesethi enkulu njengoko:
{0, 2, 4, 6, 8, ..., 94, 96, 98, 100}
I-ellipsis ibonisa ukuba umzekelo - nokuba ngamanani kuphela - uyaqhubeka ngecandelo elingabhaliweyo liseti.
Izakhelo ezizodwa
Iiseti ezizodwa ezisetyenziswa rhoqo zichongwa ngokusebenzisa iileta ezithile okanye iimpawu. Ezi ziquka:
- Ø okanye {} - isethi esingenalutho - isethi esinazo izakhi ;
- U -isethi yehlabathi jikelele - isethi equle zonke izicwangciso ezinxulumene nencazelo ethile ;
- Z - isethi yazo zonke iinombolo: Z = { ... , -3, -2, -1, 0, 1, 2, 3, ... };
- Izinombolo zendalo ze- N (iinombolo ezintle): N = {0, 1, 2, 3, 4, 5, ... }.
IQela kunye neendlela ezichazayo
Ukubhala okanye ukubeka uluhlu lwezinto ezisetyenzisiweyo, ezifana nesethi yeeplanethi zangaphakathi okanye zomhlaba kwi-system yethu yelanga, ibhekiselwa kuxwebhu lokubhala okanye indlela yokuhamba .
T = {mercury, venus, umhlaba, mars}
Enye inketho yokuchonga izixhobo zesethi usebenzisa indlela echazayo, esebenzisa inqaku elifutshane okanye igama ukuchaza isethi ezifana:
T = {iiplanethi zasemhlabeni}
I-Notation-Builder Notation
Enye indlela eya kwindlela kunye neendlela ezichazayo kukusebenzisa ukukhishwa kwe-set-builder , eyindlela efutshane yokuchaza umgaqo wokuba imimiselo yesetyenti ilandele (umgaqo owenza ukuba amalungu athile athile) .
Ukukhangela-ukwakha umakhi wokubeka isethi yamanani okwenyama ngaphezu kwe-zero ngu:
{x | x ∈ N, x > 0 }
okanye
{x: x ∈ N, x > 0 }
Kwi-notation-builder notation, ileta "x" yinto eguqukileyo okanye indawo yokuhlala, enokuthi ithatyathelwe nayiphi na enye incwadi.
Shorthand Characters
Iimpawu ze-Shorthand ezisetyenziselwa ukuphawula okuyi-setti ziquka:
- Ibha yomgca okanye ikholoni ( | okanye okanye : abalinganiswa) - ngabahluli bafundwa ngolu hlobo;
- I-lowercase epsilon ( ∈ uhlamvu) - ifundwa njengento yinto;
- I-character - ifundwa njengeyona nto yinto.
Ngoko, {x | x ∈ N, x > 0 } iza kufundwa njenge:
"I setethi yazo zonke, x efana nokuba x iyinxalenye yesethi yamanani engokwemvelo kwaye x inkulu kune-0."
Imisimbozo kunye neVenn Diagram
Umzobo weVenn - ngamanye amaxesha ubizwa ngokuba ngumzobo othethiweyo - usetyenziselwa ukubonisa ubudlelwane phakathi kwezinto zeesethi ezahlukeneyo.
Emfanekisweni ongasentla, icandelo eligqityiweyo lomzobo weVen ubonisa indlela yokuhamba phakathi kwee-E ne-F (izinto eziqhelekileyo kwiisethi zombini).
Ngaphantsi kweloludwe lubhalwe uphawu lokuqulunqwa komakhi (umsebenzi ongezantsi "U" uthetha intsebenziswano):
E ∩ F = {x | x ∈ E , x ∈ F}
Umda womxholongwane kunye neleta U ekhoneni lomzobo weVen ubonisa isethi yonke yezinto eziphantsi kokuqwalaselwa kulo msebenzi:
U = {0, 1, 2, 3, 4, 6, 8, 12}