Kodi inteja zabwino? History, ukulu, maonekedwe

Masamu wosiyana nzeru ndi ambiri za zana lachisanu ndi chimodzi BC. e., ndipo kuchokera nthawi imeneyo anayamba ulendo wake wopambana padziko lonse. Gawo lirilonse la chitukuko anabweretsa zinthu zatsopano - ndi maziko chifukwa cha kusintha, lidzasinthidwa ndi masiyanidwe ndi yofunika kakyulasi m'ma alternated, njira anayamba zosokoneza, ndi kubwera nthawi pamene "chiyambi cha masamu ovuta kwambiri -. Yasowa kwa manambala onse" Koma zomwe zinali kumbuyo?

Mfundo poyambira

Manambala zachilengedwe anali pa ndime ndi woyamba ntchito masamu. Kamodzi kumbuyo, awiri kumbuyo, atatu msana ... Iwo anaonekera chifukwa cha wasayansi Indian amene oyamba Pamalo dongosolo chiwerengero. Mawu "Pamalo" zikutanthauza kuti malo lililonse manambala angapo a mosamalitsa kumatanthauza ndi limafanana ndi gulu lake. Mwachitsanzo, manambala 784 ndi 487 - manambala ndinu yemweyo, koma manambala si mofanana zakale zikuphatikizapo 7 mazana, pamene lachiwiri - 4. yekha luso Indians anatola Aluya, amene anakulira chiwerengero cha mitundu imene tikudziwa tsopano.

Kale, manambala Ufumuyo tanthauzo lachinsinsi, katswiri wa masamu kwambiri Pythagoras ankakhulupirira kuti chiwerengero ndi pa mtima wa chilengedwe pa ndime ndi zinthu zofunika - moto, madzi lapansi, mpweya. Ngati tikambirana zonse yekha ndi mbali masamu, ndiye kuti ndi inteja zabwino? m'munda wa manambala lachibadwa amaimira monga N ndipo ndi wopandamalire mndandanda wa manambala amene integers zabwino ndi 1, 2, 3, ... + ∞. Zero Kwaletsedwa. Makamaka ntchito kuwerengera zinthu ndi kukhazikitsa dongosolo.

ndi zimene ambiri achilengedwe mu masamu? axioms wa Peano

Field N ndi patsinde pa zomwe apuma masamu pulayimale. M'kupita kwa nthawi, wakutali integers kumunda, manambala zomveka, zovuta manambala.

Ntchito ya masamu Italy Dzhuzeppe Peano linachititsa structuring zina za masamu apanga iye mwambo nakonza pansi zake zina kuposa munda dera N. Kodi nambala zachilengedwe, izo zapezeka kale osavuta, zotsatirazi tikambirana pamaziko a tanthauzo masamu wa Peano axioms.

• Unit amaonedwa monga nambala achilengedwe.
• nambala yotsatira nambala achilengedwe, ndi zachilengedwe.
• Pamaso wagawo ndi nambala achilengedwe.
• Ngati nambala b ayenera kukhala chiwerengero c, ndi chiwerengero cha anthu d, ndiye m'ma = d.
• The axiom wa kupatsidwa ulemu, womwe chakuti chiwerengero zachilengedwe, ngati mawu zimadalira chizindikiro ndi zoona kwa chiwerengero 1, ndiye tiyenera kuganiza kuti ntchito N Chiwerengero cha minda ya manambala zachilengedwe N. Kenako amanena ndi zoona kwa N = 1 ku munda wa manambala zachilengedwe N.

zikuluzikulu munda wa manambala zachilengedwe

Kuyambira kumunda N anali oyamba masamu, ndi kuwaona monga ulamuliro wa tanthauzo, ndi malo pansipa chiwerengero cha wotuluka mfundo. Iwo anatseka ndipo palibe. Chachikulu kusiyana ndi opareshoni kungakupatseni kusiya chifukwa chatsekedwa mkati kuika N, mosasamala chimene manambala ali nawo. Ndi moti chilengedwe. Zotsatira za mogwirizana otsala n'zosangalatsa kumva si monga m'mbali ndipo zimadalira chakuti kwa anthu amene amachita akuti, ngati kungakhale mosiyana ndi tanthauzo zofunika. Choncho, ntchito kutseka:

• Kuwonjezera - × + Y = z, kumene ×, Y, z ali ku munda N;
• chulutsa - × * Y = z, kumene ×, Y, z ali ku munda N;
• exponentiation - × ^Y, kumene ×, Y ndi ku N. Field

The ntchito otsala chifukwa cha zomwe sangaonekerenso mtima wa nkhani "kuti ndi nambala chachibadwidwe" motere:

• Wochotsera - × - Y = z. Field manambala zachilengedwe chololera pokhapokha ngati yaitali × Y;
• Chigawo - × / Y = z. Field manambala zachilengedwe chololera pokhapokha ngati z lagawidwa ndi Y palibe zotsalira, i.e. wogawana.

Katundu wa manambala, yoperekedwa kwa munda N

Onse zina maganizo masamu udzakhala wokhazikika pa katundu awa, ambiri zazing'ono, koma palibe kwenikweni.

• Commutative chuma cha Kuwonjezera - × + Y y n'zofanana + ×, kumene chiwerengero cha ×, Y m'gulu bokosi N. Kapena odziwika bwino "pa yosamutsa a ndalama ndi sanasinthe."
• Commutative chuma cha chulutsa - × * Y = Y * ×, kumene manambala ×, Y ndi ku N. Field
• Associative chuma cha Kuwonjezera - (× + Y) + z = × + (Y + z), kumene ×, Y, z ali ku N. Field
• Associative chuma cha chulutsa - (× * Y) * z = × * (Y * z), kumene manambala ×, Y, z ali ku N. Field
• distributive katundu - × (Y + z) = × * Y + × * z, kumene manambala ×, Y, z ali ku N. Field

Zamkatimu Pythagoras

Chimodzi mwa zinthu zoyambirira mu chidziwitso cha ophunzira mu nyumba ya pulayimale masamu pambuyo kumvetsa okha manambala amatchedwa achilengedwe, ndi gome la Pythagoras. Izo zikhoza kuganiziridwa osati ku mawonedwe a sayansi, komanso lofunika chipilala sayansi.

Izi tebulo chulutsa kakusintha kusintha pa nthawi: inachotsedwa ziro, ndi manambala kuyambira 1 mpaka 10 kuima okha, kupatulapo malamulo zoopsa (mazana, zikwi ...). Ndi tebulo lomwe maudindo a mizere ndi mizati - chiwerengero ndi nkhani za maselo a mphambano uli wofanana ndi mankhwala zawo.

Mu mchitidwe kuphunzitsa otsiriza zaka zochepa panali kufunika kuphunzira tebulo Pythagorean "kuti", ndiye, anapita pa kuloweza. Chulutsa 1 zasiyidwa, kuyambira zotsatira ndi wofanana 1 wamkulu chinthu. Nthawiyi, tebulo Tingaone ndi wamaliseche diso chitsanzo: mankhwala a manambala kuwonjezeka ndi sitepe imodzi, umene uli wofanana mutu chingwe. Choncho, chinthu chachiwiri akutionetsa kangati muyenera choyamba, kuti akapeze mankhwala ankafuna. dongosolo ndi wosiyana ndi munthu yabwino kwambiri chimene chinalipo Zapakati: ngakhale kudziwa kuti ndi inteja zabwino, ndi momwe izo ziriri zazing'ono, anthu anatha kusokoneza nokha tsiku ndi tsiku ndi ntchito dongosolo kuti zinali zochokera madigiri awiri.

A kagawo monga chopunthira cha masamu

Pa nthawi, munda wa manambala zachilengedwe N imatengedwa okha monga mmodzi wa subsets a manambala zovuta, koma izo sizimapanga iwo zochepa wapatali sayansi. Natural chiwerengero - chinthu choyamba chimene mwana amaphunzira kuphunzira tokha ndi dziko lonse. Kamodzi chala, awiri chala ... Ndiyamika iye, munthu anapanga ndi kulingalira, komanso luso kudziwa chifukwa ndi zotsatira za linanena bungwe, amaika mumsewu njira atulukira lalikulu.