Keeb kwm ntawm tus xov tooj zero. Yuav ua li cas yog lub xov tooj 0?

Qhov yuav tsum tau rau suav los ua khees mus rau tus neeg los ntawm thaum pib ntawm lub tsim ntawm lub txheej thaum ub cov haiv neeg. Lawv hais txog zauv tshuab, nrog kev siv numerals, tsim rau hauv tag nrho cov cais chaw ntawm civilization nyob rau hauv Iyi tebchaws, thiab ancient Babylon, Tuam Tshoj thiab Is Nrias teb, thiab South American Indians nyob rau hauv ancient Greece. Kev kawm txog zauv tau tsim los ntawm ib tug yooj yim count ntawm tej yam khoom daws txoj kev tshawb xav topology. Nyob rau hauv cov ntaub ntawv no, zaj dab neeg txog pes tsawg lawm xwb ib tug me me feem ntawm lub sij hawm no.

Numbers thiab cov nuj nqis

Los ntawm cov Latin nullis ( "tsis muaj") yog lo lus rau ib yam ntawm cov tseem ceeb tshaj plaws leb. Nws muaj xws li tsis tau tsuas yog ib lub cim - ib daim duab uas yuav pab kom tau, cov ntaub ntawv zauv hauj lwm. No tag nrho tswvyim. Qhaj ntawv ntawm tej nqi, lub emptiness, qhov pib thiab qhov infinite - ib tug philosophical cwj pwm rau cov tswv yim nyob txawv nyob rau hauv txawv eras, nyob rau hauv txawv tshuab worldview.

Positional tooj system

Nyob rau hauv prehistoric lub sij hawm, calculus pab kom cov ntiv tes thiab ntiv taw. Faib xov tooj nyob rau hauv lub fives thiab kaum, lub keeb kwm ntawm lub decimal tooj system yog hais txog rau qhov no. Nyob rau hauv lub neej yav tom ntej, nyob rau hauv thiaj li yuav pab txhawb cov kev ua hauj lwm, nyob rau hauv lub chav kawm tau nicks rau ntoo thiab tsiaj cov pob txha, serifs rau lub pob zeb, pebbles. shells thiab lwm yam me me khoom. Txhua xws caij nruab nrab yog ib lub xov tooj. Zoo ib yam li xwm yog cov feem ntau cov tswv yim hais txog zauv qauv. Tej systems yog hu ua positional - tus nqi xov tooj thaum uas sau ntawv xov tooj txiav txim los ntawm lawv txoj hauj lwm los yog tawm.

Ib qho piv txwv ntawm cov lus rov mus kom ze, thiab tseem siv system yog ib txoj kev sau ntawv xov tooj tau tuaj lawm txij thaum lub sij hawm ntawm ancient Rome. Nyob rau hauv nws rau xaiv units, kaum, pua pua thov ntawv ntawm lub Latin niam ntawv.

abacus

Audit board, muaj raws ntawm qho to coj mus rau tej qhov chaw, nyob rau hauv uas yog muab tso rau pebbles los yog cov hlaws dai, yog paub mus rau lub haiv neeg ntawm txawv haiv neeg thiab epochs. Nws muaj lwm yam ntau ntau yam ntawm abaca - ib tug hlua nrog cov pob caus ntawd los yog cords nrog cov hlaws dai. Cov theem tom ntej nyob rau hauv txoj kev loj hlob ntawm xws li ua cov qhab nia uas yog hais siv ua ntej lub advent ntawm cov cav laij leb.

Keeb kwm ntawm lub xov tooj ntawm cov voj - yog tus txheej txheem ntawm tsim ntawm zauv tswv yim thiab pib ntawm txoj kev siv ntawm lub cim, cim tias seb thaum nws. Thiab lub abacus, thiab cov qhab nia yog, nyob rau hauv ib lub siab, thiab ib tug txhais tau tias ntawm visualization ntawm suav series. Npliag qhov chaw nyob rau hauv cov coj ua si nraum zoov los yog uas ploj lawm knuckle nyob ua paub daws teeb tswvyim ntawm xoom tseeb nyiaj. Lub cim txhais tau tias nws xub tshwm sim nyob rau hauv ancient Babylon mathematicians thiab astronomers.

Babylon tsis muaj dabtsis cim

Nyob rau hauv kev vam meej, yug ntawm lub Tigris thiab Euphrates, tau txais los ntawm ib tug zauv system pub los ntawm cov ancient Sumerians. Nws yog positional - tus nqi xov tooj nyob ntawm seb txoj hauj lwm nyob rau hauv kev sib raug zoo mus rau lwm cov xov tooj. Tsim rau 4-5 txhiab xyoo BC. e., nws yeej ua tau rau tus xov tooj 60. Lub zauv uas siv los ntawm lub ancient Babylonian astronomers thiab engineers tau saib heev li loj thiab xis nyob. Yuav kom ntse lis cov xov tooj, nws yog tsim nyog los cim los yog kom ua ntej lub qhov muag ntawm tus npaug ntawm tag nrho cov zauv los ntawm 1 mus rau 60.

Cov zero los yog kos npe rau, yuav qhia ib tug tau txais Babylonians paug nyob li ob txheej angled npoo los yog cov xub. Qhov no cim tau ib feem ntawm thiab tsis koom nyob rau hauv xam ua hauj lwm - ntxiv los yog muab los ntawm nws tsis yog.

txawv teb chaws xoom

Txawm li cas los ntawm koj daim ntawv thom nug Mesopotamia pes tsawg coined lub Khab ntawm Central America - Maya thiab Incas. Common rau ob leeg tooj tshuab yog hais tias lawv tsis tsim lub tswv yim pes tsawg raws li ib tug xov tooj.

Drevneamerikanskaya civilization tau sab laug lub ntiaj teb no ib tug ntau ntawm cov achievements nyob rau hauv kev txawj ntse kheej. Complex Mayan daim ntawv qhia hnub system thiab lub Incas - qhov tshwm sim ntawm centuries ntawm kev nyob rau hauv astronomical tswvyim thiab nyuab zauv. Tiam sis yeej tsis nyob rau hauv lawv cov sib npaug, tus xov tooj pes tsawg yog tsis tam sim no raws li ib tug xov tooj ntawm influencing lub txiaj ntsim ntawm zauv ua hauj lwm.

antique saib

Lub ntsiab legacy ntawm lub ancient Greek mathematicians muaj cov achievements nyob rau hauv geometry thiab astronomy. Numbers nyob rau hauv lawv cov kev nthuav qhia - yog theem uas muaj ib tug pib, ib tug kawg thiab ib tug predetermined ntev. Xoom - ib tug xov tooj uas tsis muaj nyob rau hauv cov ntaub ntawv no, lub tswv yim muaj nuj nqis. Ya nrog pes tsawg ntev nyob rau hauv ancient lej thiab philosophy tsis ua kev zoo siab.

Ib tug ntawm lub ntsiab tenets ntawm Aristotle cov lus qhuab qhia yog ib co lus Natura abhorret lub tshuab nqus tsev - "Xwm abhors ib lub tshuab nqus tsev." Infinity, nothingness, uas tsis yog-hav zoov - cov pawg ua tsis haum mus rau hauv lub ancient ntug. Yog li ntawd, niaj hnub ntsiab lus ntawm cov lo lus nug "li cas tus xov tooj yog 0" yog tsis field rau Archimedes, Pythagoras los yog Euclid, txawm hais tias zoo ib yam li lub voj cim yog pom nyob rau hauv lub rooj ntawm qhov zoo astronomer Ptolemy. Tsab ntawv "Omicron" (thawj tsab ntawv nyob rau hauv lo lus οὐδέν - "tsis muaj dab tsi"), nws yuav tsum tshwm sim nyob rau hauv lub empty hlwb.

Teb koj chaw zero - Is Nrias teb

Yuav ua li cas Indian mathematicians yees? Mahavira (850), Brahmagupta (1114), Aryabhata (476) - sau ntawm lub treatise, uas lom zem ntau coj zoo lub niaj hnub system ntawm kev sau ntawv xov tooj thiab cov kev cai ntawm yooj yim xam hauj lwm. Historians ntseeg hais tias tus zauv system tau borrowed los ntawm Suav Khab, thiab qhov xwm ntawm nws txoj hauj lwm - los ntawm poob rau Npanpiloo. Nws yog ntseeg hais tias lub zero cim twb tseem borrowed los ntawm cov neeg Qhab ntawm lub chaw ua hauj lwm ntawm Ptolemy.

Tus thawj mathematician uas formulated ib tug tag nrho hais txog zauv system, uas yog tseem lawm thiab ua hauj lwm pab lub ntau dua ib feem ntawm tib neeg, yog Mohammed Rau Hauv Musa Khwarizmi (787-850), uas nyob rau hauv Baghdad. Nyob rau hauv nws "Phau Ntawv Indian account" cuaj Arabic numerals yog piav nyob rau hauv kev nthuav dav thiab teb cov lus nug: "Yog lub xov tooj ntawm 0?" Pav pes tsawg nyob rau hauv phau ntawv no yog suav tias yog lub ua ntej. Latin txhais lus ntawm no ua hauj lwm, tau ua lug paub nyob rau hauv cov teb chaws Europe nyob rau hauv lub xyoo pua XII thiab pw lub hauv paus rau cov kis ntawm sab hnub tuaj zauv paub.

Tsis zoo li cov Europeans, ib tug mus ib txhis nyob rau hauv lub sab hnub tuaj philosophers evoked awe. Yog li ntawd, lub voj nyob rau hauv qhov sib npaug ntawm ancient Indian zaum tsis tau tsuas yog ua qhov kawg lub cim ntawm cov tsis muaj units nyob rau hauv coj txaus qhia, tab sis kuj yog ib tug natural tooj, rau qhov tshwm sim ntawm lub xam. Qhov sib ntxiv ntawm xoom, muab los ntawm 0 - tag nrho cov no tau pom tus nqi ntawm muaj nuj nqis zauv hauj lwm.

Needless sau ntawv xov tooj ntawm 1 mus rau 0 tau tau kawg zoo li kuj ua tsaug rau ancient Indian zauv treatises, thiab lub cim, zoo li cas yog hu ua nyob rau hauv Arabic nyob rau hauv Teb chaws Europe, cov koom pheej hu ua Indian.

Lub keeb kwm ntawm "zero" tus xov tooj yog thaws rov los nyob rau hauv lub etymology ntawm qhov yooj yim xaam nqe lus. Lo lus "daim duab" muaj Arabic cov hauv paus hniav thiab yog muab tau los ntawm lo lus "al-Sifre," uas txhais tau tias "npliag, pes tsawg." English "zero" vaguely zoo xws li cov "marshmallow" - cov cua los ntawm sab hnub tuaj - nws yog los ntawm East rau teb chaws Europe tuaj finalization, muaj kuab thiab yooj yim tooj system.

Arabic numerals nyob rau hauv cov teb chaws Europe

Ib tug ntawm lub ntsiab promoters ntawm lub as European cov system yog tus naas ej Italian mathematician Leonardo Fibonacci. Nws ua hauj lwm "liber Abaci" (1202) qhia cov European zaum nrog cov cim thiab cov kev cai uas lub koom pheej sau zauv hauj lwm. Tus thawj yooj yim thiab rationality sab hnub tuaj zauv qauv menyuam los ntawm cov neeg uas yeej ib txwm mloog txhua txhua hnub kev kho mob nrog cov zauv - lub bankers thiab traders. Lawv sai sai txais yuav los ntawm As tub txawj tub ntse numbering system thiab sau ntawv xov tooj. Tab sis nyob rau hauv txoj kev xyaum ntawm science nyob rau hauv cov teb chaws Europe txoj kev paub no yog nrees tsuas yog los ntawm lub xyoo pua 4, hloov lub me nyuam los tu ntawm European mathematicians ntawm lub ancient system.

Nws muaj gained tseem ceeb nrog cov kev taw qhia ntawm ib tug pes tsawg nyob rau hauv lub scientific siv cov lub coordinate system, npaj nyob rau hauv lub xyoo pua XVII Rene Descartes. Xoom yog pov tseg nyob rau hauv qhov chaw, tus nqi mas yuav kis tau pom thiab tsis pom kev to taub siv taw tes rau ntawm peb axes.

Nyob rau hauv Russia qhia ib tug pes tsawg nyob rau hauv kev xyaum dag zog Leontiya Magnitskogo, tus naas ej sau ntawm cov phau ntawv nyeem "xam, uas yog hais tias qhov kev kawm tus nab npawj" (1703).

zog xoom

Zero, uas demarcates ob zoo thiab tsis zoo tus xov tooj, muaj cim zauv zog. Nws yog ib qho xov tooj, tsis muaj integer muaj ib tug zoo kos npe rau. Ntxiv thiab rho tawm nrog xoom xoom tsis cuam tshuam rau tus xov tooj thiab muab los ntawm 0 muab pes tsawg. Cov kev faib los ntawm xoom yog ib tug meaningless lag luam, uas nyob rau hauv cov ntaub ntawv ntawm siv nyob rau hauv ib qho computer program yuav ua rau kuv haj puas tsuaj rau lub system.

Nws yog nyob rau hauv ib qho kev sim faib los ntawm 0 muaj pov thawj los ua ib tug tsis ua hauj lwm taw tes rau hauv lub computer system ntawm lub US Navy cruiser "Yorktown", uas tshwm sim nyob rau hauv lub caij nplooj zeeg ntawm 1997 thiab coj mus rau lub tso cai shutdown ntawm lub propulsion system. Incorrectly muaj feem xyuam rau tus xov tooj, lub ntsiab lus "tsis muaj dab tsi", tau ua ib tug haib warship nyob rau hauv tsis paub pab nyob ruaj ruaj hom phiaj.

Tus nqi ntawm no tus xov tooj yog ho ntau zog rau txoj kev loj hlob ntawm science. Xoom tshwm sim nyob rau hauv cov cheeb tsam ntawm tsis tsuas yog purely zauv. Hnov pib nyob rau hauv acoustics yuav 0. Uas tooj yog nyob rau hauv thaum pib ntawm lub scale ntawm ntau measuring pab kiag li lawm, lub npe hu thiab schoolboy: 0 rau Celsius - lub freezing point ntawm dej, thaum pib ntawm suav longitude - pes tsawg caij nyoog nruab nrab thiab thiaj li tawm ..

Binary numeration, uas tau txais kev pab raws li lub hauv paus rau lub creation ntawm niaj hnub xam pab kiag li lawm yog ib tug positional tooj system nrog puag ob tug. Qhov no txhais tau tias tag nrho cov ntaub ntawv mus rau hauv ib lub computer system, yog encoded los ntawm ib tug ua ke ntawm ob cim - ib tug thiab pes tsawg.

Lub luag hauj lwm nyob rau hauv lub niaj hnub ntiaj teb no ntawm computers yuav decisive rau tag nrho cov yam ntawm lub neej thiab, yog li ntawd, lub keeb kwm ntawm tus xov tooj pes tsawg, tsis muaj uas lawv cov tsos yuav tau tsis yooj yim sua, tseem.