No ke aha ʻaʻole mākou e puʻunaue me ka ʻole?
Nā mea
E noʻonoʻo paha ka poʻe heluhelu no ke aha wau e hāʻawi ai i kahi ʻatikala holoʻokoʻa i kahi pilikia banal? ʻO ke kumu o ka nui o nā haumāna (!) e hana maʻamau i ka hana ma lalo o ka inoa. A ʻaʻole nā haumāna wale nō. I kekahi manawa hopu au a me na kumu. He aha ka mea e hiki ai i nā haumāna o ia mau kumu ke hana i ka makemakika? ʻO ke kumu koke o ke kākau ʻana i kēia kikokikona, ʻo ia ke kamaʻilio ʻana me kekahi kumu, ʻaʻole pilikia ka mahele ʻana me ka ʻole ...
Me ka ʻole, ʻae, koe wale nō ka pilikia o ka mea ʻole, no ka mea ʻaʻole pono mākou e hoʻohana iā ia i kēlā me kēia lā. ʻAʻole mākou e hele kūʻai i nā hua manu ʻole. "Hoʻokahi kanaka i loko o ka lumi" kani maoli, a ʻo "zero poʻe" kani maoli. Wahi a ka poʻe ʻōlelo ʻōlelo, aia ka zero ma waho o ka ʻōnaehana ʻōlelo.
Hiki iā mākou ke hana me ka ʻole o ka zero i loko o nā waihona waihona pū kekahi: hoʻohana wale - e like me ka thermometer - ʻulaʻula a me ka uliuli no nā waiwai maikaʻi a maikaʻi ʻole (e hoʻomanaʻo no ka mahana he mea kūlohelohe ia e hoʻohana i ka ʻulaʻula no nā helu maikaʻi, a no nā waihona kālā. ʻo ia ka ʻaoʻao ʻē aʻe, no ka mea e hoʻomaka ka hōʻaiʻē i kahi ʻōlelo aʻo, no laila ʻoi aku ka ʻulaʻula).
Ma ka hoʻokomo ʻana i ka zero ma ke ʻano he helu kūlohelohe, hoʻopā mākou i ka pilikia o ka ʻokoʻa Nā helu kardinal od hale hale. Ma loko o 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, …..
ua like ka mana o ka helu me ka helu o kahi e ku ai. A i ʻole, aia ia ma ke kaʻina 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, …..
ʻO ka helu o nā sets singleton e hele mai i ka lua, ʻo ka helu o nā set me ʻelua mau mea hele mai ke kolu, a pēlā aku. Pono mākou e wehewehe i ke kumu, no ka laʻana, ʻaʻole mākou e helu i nā wahi o nā mea pāʻani i nā hoʻokūkū mai ka wā ʻōpio. A laila e loaʻa i ka mea lanakila ma ka pae mua ka mekala kala (ua hele ke gula i ka mea lanakila ma kahi ʻole), a pēlā aku. Ua hoʻohana ʻia kekahi kaʻina hana like i ka pôpeku - ʻaʻole maopopo iaʻu inā ʻike ka poʻe heluhelu ʻo "league one" ʻo ia hoʻi " e hahai ana i ka maikai." ", a ua kapa ʻia ka zero league e lilo i "ligue nui".
I kekahi manawa lohe mākou i ka hoʻopaʻapaʻa e pono ai mākou e hoʻomaka mai ka ʻōpala, no ka mea he mea maʻalahi ia no ka poʻe IT. Ke hoʻomau nei i kēia mau noʻonoʻo, pono e hoʻololi ʻia ka wehewehe ʻana o kahi kilomika - ʻo ia ka 1024 m, no ka mea ʻo ia ka helu o nā bytes i ka kilobyte (E kuhikuhi wau i kahi ʻakaʻaka i ʻike ʻia e nā ʻepekema kamepiula: "He aha ka ʻokoʻa ma waena o kahi kanaka hou a me he haumāna o ka ʻepekema lolouila a he haumāna makahiki ʻelima o kēia kumu? ʻo ka kilobyte he 1000 kilobytes, ʻo ka hope - ʻo ka kilobyte he 1024 mika")!
ʻO kahi manaʻo ʻē aʻe, pono e noʻonoʻo nui ʻia, ʻo ia kēia: ke ana mau mākou mai ka ʻōpala! Ua lawa ka nānā ʻana i kēlā me kēia unahi ma ke aliʻi, ma nā unahi hale, ʻoiai ma ka uaki. Ma muli o ke ana ʻana mai ka ʻaʻole, a hiki ke hoʻomaopopo ʻia ka helu ʻana ma ke ʻano he ana me kahi ʻāpana ʻole, a laila pono mākou e helu mai ka ʻole.
He mea maʻalahi, akā...
E haʻalele kākou i ka noʻonoʻo maʻamau a hoʻi i ka mahele me ka ʻole. He maʻalahi ka mea a he maʻalahi inā ʻaʻole no ... no laila he aha? E noʻonoʻo kākou a hoʻāʻo. ʻEhia ka nui - puʻunaue hoʻokahi me ka ʻole? E nana kakou: 1/0 = x. E hoonui i na aoao elua me ka helu o ka aoao hema.
Loaʻa iā mākou 1 = 0. Ua hewa kekahi mea! He aha lā? Ah manaʻo! ʻO ka manaʻo e loaʻa ka quotient o ka lokahi a me ka zero e alakaʻi i kahi kūʻē. A inā ʻaʻole hiki ke puunaue ʻia kekahi me ka ʻole, hiki i kekahi helu ke hiki. Inā ʻoe, e ka mea heluhelu, e ʻohi ʻoe i kou poʻohiwi a e haʻohaʻo i ke kumu e kākau ai ka mea kākau (ʻo ia hoʻi, ʻo wau) e pili ana i ia mau ʻōlelo palaka, a laila ... hauʻoli loa wau!
Hiki ke pale ʻia ke kumu 0/0 = 0 ma ke kumu paʻakikī, akā kūʻē ia i ka lula ʻo ka hopena o ka puʻunaue ʻana i kahi helu iā ia iho ua like ia me hoʻokahi. ʻOiaʻiʻo, akā ʻokoʻa loa nā hōʻailona e like me 0/0, °/° a me nā mea like i ka helu helu. ʻAʻole lākou manaʻo i kekahi helu, akā he mau hōʻailona hōʻailona no nā kaʻina o kekahi mau ʻano.
I loko o kahi puke ʻenekinia uila, ua ʻike au i kahi hoʻohālikelike hoihoi: ʻo ka puʻunaue ʻana me ka zero e like me ka pōʻino e like me ka uila uila kiʻekiʻe. He mea maʻamau kēia: Ua ʻōlelo ke kānāwai o Ohm ua like ka lakio o ka volta a me ke kū'ē i kēia manawa: V = U / R. Inā ʻaʻole ke kūʻē ʻana, e kahe ka au i ka manaʻo ʻole ma o ka mea hoʻokele, e puhi ana i nā mea hoʻokele a pau.
Ua kākau wau i kekahi mele e pili ana i ka pōʻino o ka puʻunaue ʻana me ka ʻole no kēlā me kēia lā o ka pule. Hoʻomanaʻo wau ʻo ka lā nui loa ʻo ia ka Pōʻalima, akā minamina i kaʻu mau hana āpau ma kēia wahi.
Ke puunaue oe i kekahi mea me ka zero
Poakahi loa
He pule ka mea i hanaia
Ua hāʻule nui ʻoe.
I ka auina la Poalua
Hoʻokomo ʻoe i ka zero i ka denominator
E hai aku au ia oe, ua hewa oe
Ka makemakika ino!
I ka wā ʻaʻole, ma o ka perversion,
Makemake ʻoe e māhele i ka Pōʻakolu
E loaʻa iā ʻoe ka pilikia nui
Loaʻa iā ʻoe ka mauʻu a me ka wai ma kou poʻo!
ʻO kekahi Bartek me mākou.
Ua kūʻē ʻo ia i nā lula.
Ma ka Poaha, hiki ke puunaueia me ka zero.
ʻAʻole ʻo ia ma waena o mākou!
Inā loaʻa iā ʻoe kahi kuko ʻē
E puunaue me ka zero ma ka Poalima
E ʻoiaʻiʻo wau, e ʻoiaʻiʻo wau:
ʻino ka hoʻomaka ʻana i kēia hopena pule.
I ka wā ʻaʻole, ma kahi o ka Pōʻaono
Na ʻoe ka mea hoʻokaʻawale (ʻaʻole wiwo ʻole)
E kukuli malalo o ka pa halepule.
ʻO kou alahouana kēia.
Makemake ʻoe i ka zero ma lalo o ka pā,
E hoʻomaha i ka lā Sābati
E lawe mai i ka peni, papa ʻeleʻele.
Kākau: ʻaʻole hiki ke puʻunaue ʻia me ka ʻole!
Hoʻopili ʻia ʻo Zero me ka ʻole a me ka ʻole. ʻOiaʻiʻo, ua hele ʻo ia i ka makemakika ma ke ʻano he nui, ke hoʻohui ʻia i kekahi, ʻaʻole ia e hoʻololi: x + 0 = x. Akā i kēia manawa ua ʻike ʻia ka zero i nā waiwai ʻē aʻe, ʻoi aku ka nui hoʻomaka unahi. Inā ma waho o ka puka makani ʻaʻohe wela maikaʻi a i ʻole hau, a laila ... ʻaʻole kēia, ʻaʻole ia he manaʻo ʻaʻohe wela. ʻAʻole kahi monument zero-class i wāwahi ʻia no ka manawa lōʻihi a ʻaʻole i noho. ʻO ka mea ʻē aʻe, he mea like ia me ka Wawel, ka Eiffel Tower a me ke Statue of Liberty.
ʻAe, ʻaʻole hiki ke hoʻohālikelike ʻia ke koʻikoʻi o ka zero i kahi ʻōnaehana kūlana. Maopopo iā ʻoe, e ka mea heluhelu, ʻehia nā zeros i loaʻa iā Bill Gates i kāna waihona waihona? ʻAʻole maopopo iaʻu, akā makemake wau i ka hapalua. Me he mea lā, ua ʻike ʻo Napoleon Bonaparte ua like nā kānaka me nā zeros: loaʻa iā lākou ka manaʻo ma ke kūlana. Ma ke kiʻi ʻoniʻoni ʻo Andrzej Wajda ʻo As the Years, As the Days Go by, ua pahū ka mea pena kiʻi hoihoi ʻo Jerzy: "ʻO ka Philistine he zero, nihil, ʻaʻohe mea, ʻaʻohe mea, nihil, zero." Akā hiki ke maikaʻi ka zero: ʻo ka "zero deviation mai ka maʻamau" ʻo ia ka mea e holo maikaʻi ana nā mea a pau, a hoʻomau!
E hoʻi kāua i ka makemakika. Hiki ke hoʻohui ʻia, unuhi ʻia a hoʻonui ʻia me ka hoʻopaʻi ʻole. "Ua loaʻa iaʻu ka zero kilokani," wahi a Manya iā Anya. "A he mea hoihoi kēia, no ka mea, ua nalowale au i ke kaumaha hoʻokahi," wahi a Anya. No laila, e ʻai kākou i ʻeono mau kīʻaha hau ice cream ʻeono manawa, ʻaʻole ia e hōʻeha iā mākou.
ʻAʻole hiki iā mākou ke puʻunaue me ka ʻole, akā hiki iā mākou ke puʻunaue me ka ʻole. Hiki ke hā'awi ma'alahi i ka po'e e kali ana i ka 'ai. ʻEhia ka nui e loaʻa i kēlā me kēia?
ʻAʻole maikaʻi a maikaʻi ʻole ʻo Zero. ʻO kēia a me ka helu maikaʻi ʻoleи ʻinoʻino ʻole. Ua māʻona i nā like ʻole x≥0 a me x≤0. ʻO ka kū'ē "kekahi mea maikaʻi" ʻaʻole ia he "mea maikaʻi ʻole", akā "he mea maikaʻi ʻole a i ʻole like me ka zero". ʻO ka poʻe makemakika, kūʻē i nā lula o ka ʻōlelo, e ʻōlelo mau lākou he "like me ka zero" kekahi mea a ʻaʻole "zero." No ka hōʻoia ʻana i kēia hana, loaʻa iā mākou: inā heluhelu mākou i ke kumu x = 0 "x is zero", a laila x = 1 heluhelu mākou "x like me hoʻokahi", hiki ke ale ʻia, akā pehea ka "x = 1534267"? ʻAʻole hiki iā ʻoe ke hāʻawi i kahi waiwai helu i ke ʻano 00ʻaʻole hoʻi e hoʻokiʻekiʻe i ka zero i kahi mana maikaʻi ʻole. Ma kekahiʻaoʻao, hiki iāʻoe ke aʻa i ka zero ma ka makemake ... aʻo ka hopena e lilo mau.
Hana hoonui y = ax, ke kumu maikai o a, aole lilo i ka ole. No laila ʻaʻohe logarithm ʻole. ʻOiaʻiʻo, ʻo ka logarithm o a i ke kumu b ʻo ia ka exponent kahi e hoʻokiʻekiʻe ʻia ai ke kumu e loaʻa ai ka logarithm o a. No ka = 0, ʻaʻohe mea hōʻailona like, a ʻaʻole hiki ke lilo ka zero ke kumu o ka logarithm. Eia naʻe, he mea ʻē aʻe ka zero ma ka "denominator" o ka hōʻailona o Newton. Manaʻo mākou ʻaʻole alakaʻi kēia mau ʻaha kūkā i kahi kūʻē.
hoike wahahee
He kumuhana maʻamau ka māhele ʻana i ka ʻole no nā hōʻike wahaheʻe, a hiki i nā poʻe makemakika akamai. E hāʻawi wau iā ʻoe i ʻelua o kaʻu mau hiʻohiʻona punahele. ʻO ka mua he algebraic. E "hōʻoia" au ua like nā helu a pau. Inā paha ʻelua mau helu like ʻole. No laila, ua oi aku kekahi o lakou i kekahi, e a > b. E manaʻo kākou ʻo c ko lākou ʻokoʻa
c \uXNUMXd a - b. No laila, loaʻa iā mākou a - b = c, no laila a = b + c.
Hoʻonui mākou i nā ʻāpana ʻelua o ka hope me ka a - b:
a2 – ab = ab + ac – b2 – bc.
Unuhi au i ka ak i ka aoao hema, oiaio, hoomanao au i ka hoololi ana i ka hoailona:
a2 - ab - ac = ab - b2 - bc.
Hoʻokuʻu wau i nā mea maʻamau:
A (a-b-c) \uXNUMXd b (a-b-c),
Kaʻana like a loaʻa iaʻu kaʻu mea i makemake ai:
a = b.
A ʻoiai he malihini, no ka mea, ua manaʻo wau he > b, a loaʻa iaʻu kēlā a = b. Inā ma ka laʻana ma luna o ka "hoʻopunipuni" maʻalahi ke ʻike, a laila ma ka hōʻike geometric ma lalo ʻaʻole maʻalahi. E hōʻoia wau ʻaʻole ... ʻaʻohe trapezoid. ʻAʻole i loaʻa ka kiʻi i kapa ʻia he trapezoid.
Akā, e manaʻo mua aia kekahi mea e like me kahi trapezoid (ABCD ma ke kiʻi ma lalo). He ʻelua ʻaoʻao like ʻole ("mau kumu"). E hohola kākou i kēia mau kumu, e like me ka mea i hōʻike ʻia ma ke kiʻi, i loaʻa iā mākou kahi paralelogram. Hoʻokaʻawale kona mau diagonal i ka diagonal ʻē aʻe o ka trapezoid i mau ʻāpana i hōʻike ʻia ka lōʻihi x, y, z, e like me ia. kiʻi 1. Mai ka like ana o na huinakolu pili, loaa ia makou na hoohalike:
kahi a mākou e wehewehe ai:
ʻO Odraz
kahi a mākou e wehewehe ai:
E unuhi i nā ʻaoʻao o ke kaulike i kaha ʻia me nā asterisk:
Hoʻopōkole i nā ʻaoʻao ʻelua me x − z, loaʻa iā mākou - a/b = 1, ʻo ia hoʻi, a + b = 0. Akā ʻo nā helu a, b ka lōʻihi o nā kumu o ka trapezoid. Inā ʻaʻole kā lākou huina, a laila ʻaʻole lākou. ʻO ke ʻano kēia ʻaʻole hiki ke loaʻa kahi kiʻi e like me kahi trapezoid! A no ka mea he trapezoids nā ʻāpana, nā ʻāpana a me nā ʻāpana, a laila, e ka mea heluhelu aloha, ʻaʻohe rhombuses, rectangles a me nā ʻāpana ...
Manaʻo Manaʻo
ʻO ka hāʻawi ʻana i ka ʻike ka mea hoihoi a paʻakikī o nā hana kumu ʻehā. Maʻaneʻi, no ka manawa mua, loaʻa iā mākou kahi mea maʻamau i ka wā o ke kanaka makua: "e manaʻo i ka pane, a laila e nānā inā koho pololei ʻoe." Ua kūpono loa kēia i ka hōʻike ʻana e Daniel K. Dennett ("How to Make Mistakes?", ma How It Is – A Scientific Guide to the Universe, CiS, Warsaw, 1997):
ʻAʻole keʻakeʻa kēia ʻano o ka "manaʻo" i ko mākou ola kanaka makua - ma muli paha o ke aʻo mua ʻana a ʻaʻole paʻakikī ke koho. Ideologically, ua like ka hanana, no ka laʻana, ma ka makemakika (piha) induction. Ma kahi hoʻokahi, "manaʻo" mākou i ke kumu a laila e nānā inā pololei kā mākou kuhi. Nīnau mau nā haumāna: “Pehea mākou i ʻike ai i ke kumu? Pehea e hiki ai ke lawe ʻia i waho?" Ke nīnau mai nā haumāna iaʻu i kēia nīnau, hoʻololi wau i kā lākou nīnau i mea hoʻohenehene: "Ua ʻike wau i kēia no ka mea he ʻoihana wau, no ka mea, ua uku ʻia wau no ka ʻike." Hiki ke pane ʻia nā haumāna ma ke kula ma ke ʻano like, ʻoi aku ka koʻikoʻi.
Mahi. E hoʻomanaʻo, hoʻomaka mākou i ka hoʻonui a kākau ʻana me ka ʻāpana haʻahaʻa, a me ka mahele me ka ʻāpana kiʻekiʻe.
ʻO kahi hui o nā manaʻo ʻelua
Ua kuhikuhi mau nā kumu makemakika ʻo ka mea a mākou i kapa ai ʻo ka hoʻokaʻawale makua ʻo ia ka hui ʻana o nā manaʻo like ʻole ʻelua. Ka hale noho i kaawale ana.
ʻO ka mea mua (Ka hale noho) i loko o nā hana kahi o ka archetype:
Māhele-māhele ʻO kēia nā hana e like me:
? (Hoʻomau mākou i ke ʻano kumu o kēia pilikia, i lawe ʻia mai ka puke lima ʻo Julian Zgozalewicz i paʻi ʻia ma Krakow i ka makahiki 1892 - ʻo ka złoty ka Rhenish złoty, ke kālā i hoʻolaha ʻia ma ka Austro-Hungarian Empire a hiki i ka hoʻomaka ʻana o ke kenekulia XNUMX).
I kēia manawa e noʻonoʻo i ʻelua pilikia me ka puke haʻawina makemakika kahiko loa ma ka Polani, makua kāne Tomasz Clos (1538). He mahele a coupe paha? E hoʻoholo i ke ʻano o nā keiki kula i ke kenekulia XNUMXth:
(Polani i ka unuhi Polani: Aia he quart a me eha ipu i loko o ka barela. He eha quarts ka ipuhao. Ua kuai kekahi i 20 barela waina no 50 zł no ke kalepa. Dute a me ka auhau (excise?) e 8 zł. kūʻai aku i ka hapahā e loaʻa ai 8 zł?)
Haʻuki, physics, congruence
I kekahi manawa ma nā haʻuki, pono ʻoe e puʻunaue i kekahi mea me ka ʻole (ratio pahuhopu). ʻAe, hoʻoponopono nā luna kānāwai. Eia nō naʻe, ma ka algebra abstract aia lākou ma ka papahana. nui ole-zeronona ka huinahalike he zero. Hiki ke wehewehe maʻalahi.
E noʻonoʻo i kahi hana F e pili ana i kahi kiko (y, 0) me kahi kiko ma ka mokulele (x, y). He aha ka F2, ʻo ia hoʻi, ka hoʻokō pālua o F? Hana Zero - he kiʻi ko kēlā me kēia kiko (0,0).
ʻO ka mea hope loa, ʻo nā kuaniti zero-zero nona ka huinahā 0, ʻaneʻane ka berena i kēlā me kēia lā no nā physicists, a me nā helu o ke ʻano a + bε, kahi ε ≠ 0, akā ε2 = 0, kāhea ka poʻe makemakika helu pālua. Loaʻa lākou ma ka helu helu makemakika a me ka geometry ʻokoʻa.
Ma hope o nā mea a pau, aia kekahi mea ma ka helu helu i mahele ʻia me ka ʻole ma ka liʻiliʻi loa o ka inoa. Mai hoʻoliʻiliʻi. E hōʻike ʻo Z i ka pūʻulu o nā helu helu. ʻO ka puʻunaue ʻana i ka set Z me ka p, ʻo ia hoʻi, ua hoʻohālikelike mākou i kēlā me kēia helu (integer) me kekahi mau mea ʻē aʻe, ʻo ia hoʻi, me nā mea i hiki ke puʻunaue ʻia ko lākou ʻokoʻa. No laila, ke loaʻa iā mākou ʻelima ʻano o nā helu e pili ana i nā helu 0, 1, 2, 3, 4 - nā koena hiki ke puunaue ʻia me 5. Ua kākau ʻia ke ʻano penei:
mod i ka wā he nui ka ʻokoʻa.
No ka = 2, elua wale no ka kakou mau helu: 0 a me 1. O ka puunaue ana i na integers i elua o ia mau papa, ua like ia me ka puunaue ana ia lakou i ka like a me ka odd. E pani kākou i kēia manawa. Māhele mau ka ʻokoʻa e 1 (mahele ʻia kekahi integer e 1). Hiki ke lawe i ka =0? E ho'āʻo kāua: i ka manawa hea ka ʻokoʻa o nā helu ʻelua he pākēneka o ka ʻole? Aia wale kēia mau helu ʻelua. No laila, ʻo ka hoʻokaʻawale ʻana i kahi pūʻulu o nā helu helu me ka zero he mea kūpono ia, akā ʻaʻole hoihoi: ʻaʻohe mea i hiki. Eia naʻe, pono e hoʻokūpaʻa ʻia ʻaʻole kēia ka mahele o nā helu ma ke ʻano i ʻike ʻia mai ke kula haʻahaʻa.
ʻAʻole pāpā ʻia ia mau hana, a me ka makemakika lōʻihi a ākea.
Laiki. 2. ʻIke i nā helu me ka hoʻohālikelike
(ʻano 5 a me ke ʻano 2)
