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Цели броеви

Module by: Liljana Stefanovska. E-mail the author

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Summary: Се воведува множеството од цели броеви

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МНОЖЕСТВО ЦЕЛИ БРОЕВИ

Со извршување на операцијата одземање, разликата на два природни броја секогаш не мора да биде природен број. Ако од природен број се одземе поголем или еднаков број, резултатот нема да биде природен број. Затоа е потребно да се изврши проширување на множеството природни броеви со додавање на бројот 00 size 12{0`} {} (нула) и негативните природни броеви: −1,−2,−3,...−1,−2,−3,... size 12{ - 1, - 2, - 3, "." "." "." } {} . Сите овие броеви го сочинуваат мно­жес­тво­то цели броеви кое се означува со ZZ size 12{Z} {}. Ако целите позитивни броеви (природните броеви) се означат со Z+Z+ size 12{Z rSup { size 8{+{}} } } {}, а целите негативни броеви со Z−Z− size 12{Z rSup { size 8{ - {}} } } {}, тогаш

Z=Z−∪{0}∪Z+Z=Z−∪{0}∪Z+ size 12{Z=Z rSup { size 8{ - {}} } union lbrace 0 rbrace union Z rSup { size 8{+{}} } } {}.

Множеството цели броеви нема ни најмал ни најголем елемент и тоа е неограничено и од лево и од десно. Тоа е исто така преброиво како и множеството на природни броеви, бидејќи неговите елементи може да се пребројат, односно да се подредат во низа по големина на следниов начин:

0,1, − 1,2, − 2,3, − 3,4, − 4,5, − 5, . . . 0,1, − 1,2, − 2,3, − 3,4, − 4,5, − 5, . . . size 12{0,1, - 1,2, - 2,3, - 3,4, - 4,5, - 5, "." "." "." } {}

Меѓу два последователни цели броја k и (k+1) не постои друг цел број.

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