Fungidzira kuti infinity inoita kunge isingagone. Nekudaro, masvomhu vanoti iyi sainzi inopa murume mukana wekuve uine isingafari "pauri." Saka, iyo samatic "Kukura kwemasvomhu," anonyora mubhuku rake, "izvi ndipo paunova mugumo" pauri. ' Uye zvakanyanya kukurwazve "pauri" neInfinity, zvirinani iwe unzwisise masvomhu. " Kuti unzwisise kuti masayendisiti aziviswa sei kusimbisa masvomhu, ngatimbokurukurai kutevedzana kwenhoroondo dzechisikigo 1, 2, 3, 4, ... Ndeipi inogona kuramba ichiperera. Maitiro ekuenderera mberi anowanzove mienzaniso yekutanga yeiyo yakaomarara pfungwa seisingafadzi. Zvichakadaro, mune masvomhu, maitiro asina muganho kana iyo yekupedzisira poindi inowanikwa kazhinji, uye mubvunzo wehupenzi pachayo unoenda nemidzi yayo mumasvomhu eGreek yekare.
Nhoroondo yeInfinity
Iyo yekutanga kuratidzira pamasvomhu infinity ingangove iyo fungidziro yemuzivi wechiGiriki weZenjon. Mumwe wavo (akanyorwa muzana remakore rechishanu kusvika kuguva yedu uye akanetseka Achilles, kukurumidza kwevaGiriki vese, izvo zvinofanirwa kumhanyisa ne turtle. Zvinoenderana neParadox, iyo inokurumidza-makumbo Achilles haizombokubata neyakafembera turtle kana turtle iri pamberi peAchilles.
Aristotle aive nehanyawo nezveizvi uye zvimwe zvisizvo zvine chekuita nekusagadzikana kusingaperi. Chisikwa, akafunga, aisakwanisa kuve akakura kwazvo. Dai zvaive zvakadaro, dai hafu yake aizove asingagumi. Asi chii chinoita kuti ifare rese rinopfuura hafu yehafu yake? Sezviri pachena, hapana chinhu; Ivo vari vaviri vasingagumi, saka panofanira kunge paine saizi imwe. Asi ivo havagone kuve vakaenzana, sehafu imwe yakasiyana. Aristotle anoisa kuendesa nhamba yezvimwe zvinopesana uye anouya kumhedziso yekuti zvakasikwa zvinofanirwa kunge zviri zvekupedzisira. Achitarisa nyeredzi pamusoro pake, anouya kumhedziso yekuti cosmos inosanganisira yakakura (asi yakadinha) nzvimbo kubva pasi iri pakati.
Nekudaro, iyo inodhura Aristotle kuratidza kuti mumwe munhu akabvunza chii kune rimwe divi renzvimbo. Zvakangodaro, iyi pfungwa yaida vanhu kweanopfuura makore chiuru, ayo kazhinji haana kushata. Muzana ramakore rechitatu BC, Archimeda akaverenga kuti majecha mangani anozoda kuzadza maAlisttle
Zvese zvachinja apo Nikolai Copernicus akataura kuti nyika haisi iyo nzvimbo yezvinhu zvakasikwa. Gare gare muzana regumi nemanomwe, Galileo Garireya seanofunga zvine ngozi, sezvo zvaive pachena zvinoratidzwa pachena. Nyika ndeyisingagumi, akazvirangarira, uye zvinhu nderekusingaperi. Vazhinji gare gare, kuma1920s, iyo German yemasvomhu David Hilbert yakauya nekuedzwa kwepfungwa kwakakurumbira kuratidza kuti zvakaoma sei kuziva pfungwa yekunzi.
Unoda kugara uchiziva nezve nhau dzichangoburwa kubva kunyika yakakurumbira sainzi uye tekinoroji mose? Nyorera kune yedu telegraph Channel kuti usapotsa zvirevo zvitsva zvitsva!
Paradox yeHotels isingaperi
Saka, ngatiti iwe uri mugamuchiri kuhotera pasi pezita rekufananidzira "risingaperi". Makamuri ese ehotera, ayo asina kugumisa vazhinji, zvizere, asi kamwe kamwe muenzi mutsva anoonekwa. Hazvifanirwe kuityaira? Kwete, zvese zvaunoda kuti ufambe muenzi kubva mukamuri 1 kuenda mukamuri 2, uye muenzi kubva mukamuri 2 iri mukamuri 3 zvichingodaro. Voila - iyo yekutanga kamuri iri yave kusununguka muenzi mutsva. Asi ko kana paine akawanda asingaperi evashanyi vatsva?
Zvinoitika kuti iwe uchiri kugona kuva nemutsa. Varimi vanobva mukamuri rekutanga vanopinda mukamuri nhamba 2, uye varimi vanobva mukamuri repiri vanopinda mukamuri vatatu uye nekuita ... kusvika pakusvika. Sezvo makamuri makamuri akapetwa kaviri, uye akazova manhamba, iwe unokwanisa kuisa maenzi mazhinji ivatsva mu (ikozvino wakasununguka) nhamba dzisina kujairika. Kunyangwe nhamba dzinofanirwa kuve dzakakura sehuwandu, sezvo paine nhamba isingaperi yemakamuri, zvisinei nekuti ivo vari kana vasinganzwisisike. Nekuda kweizvozvo, isu tinogona kuisa huwandu hwese pasina chiyero chete mu "makamuri", anogarwa nenhamba. Kuedza kwepfungwa uku kunozivikanwa sePradox yehotera isingaperi, iyo inoratidza zvakakwana zvivakwa zvezvinhu zvisina magumo.
Maererano noMusiki wenyaya yeSetiti, masvomhu Georg Kantor, kune huwandu hwakawanda, uye nhamba iyi isina kujairika inotsanangura mhando dzakawanda dzehuwandu. Semuenzaniso, muPuradox nhamba yenhamba yaive yakafanana nehuwandu hwenhamba dzisinganzwisisike (uye nhamba dzisina kujairika, uye manhamba akareruka, uye mabhiriyoni mazhinji, nezvimwewo. Nhasi zvinoita sezviri pachena, asi zvaive zvisiri pachena kuna aristotle nevateveri vake, avo vaiona infinity chaiyo yeiyo pfungwa isingagamuchiriki yesainzi.
Gadzira fungidziro - chikamu chemasvomhu, izvo zvidzidzo zvakajairika zvivakwa zveSeti - iyo zvinhu zvezvinhu zvekupokana, zvine chero zvinhu zvakajairika.
Cantor yakaratidzawo kuti nhamba yezvikamu zvakaenzana neiyi nhamba isina kusingaperi yaakadana Aleph zero. Chinhu chinoshamisa kwazvo chaakaratidza (nerubatsiro rweanonzi diagonal gakava), iro riripo kupfuura imwe nhamba isina kusingaperi.
Iwe uchafarira: Chii chinoratidza iyo Theorem yePoincare nezve kudzoka
Basa reKantor rakasangana nekuramba kukuru, asi pakupedzisira akakunda uye zvino akagamuchirwa nguva dzose. Pane vashoma vashoma vemasvomhu vanonzi intuionists kana vanogadzira vatambi vasingatendi kuti isu tinogona kunyatsonzwisisa pfungwa yehusingaperi. Muzana ramakore makumi maviri, vazivi vakabatanidzwa, vakanetseka kuti iyo cantorsky yekutarisa inogona kunzwisiswa mukurehwa. Iwe unofungei nezveizvi? Mhinduro dzichange dzakamirira pano, pamwe mukutaura kuchinyorwa ichi.