Ke kumu o ka "hua hoʻohui" "io" e haawi mai i ka "hua" Pehea e maopopo?

E hoolohe ana i ke kumu o ka makemakika, ka hapanui o nā haumāna ike i ka pono hana a me ka axiom. Akā, mau kanaka imi i ke kiʻi i ka lalo, a loaʻa mai ke kumu o ka "hua" i "hua hoʻohui" haawi i ka "hua" hoailona, a me ka wā hoonui mau io huahelu hiki mai maikaʻi.

nā kānāwai o ka makemakika

hiki ole ka hapanui o nā mākua wehewehe ana ia lakou iho, a me kā lākou mau keiki no ke aha la keia mea ai. Ka mea, paa puliki i ka mea i loko o ke kula, akā, ka mea, aole i hiki ho'āʻo i ka loaʻa mai kahi i hana ai i kēia mau rula. A no ka pono kumu. Pinepine, i ole i keia mau keiki no laila, gullible, e pono e kiʻi i ka lalo, a no ka ike, no kekahi laʻana, no ke aha la ka "hua hoʻohui" e "io" haawi "hua". A me kekahi manawa, urchins manaʻoi noi tricky nīnau, ma ka mea eʻai i ka manawa o nā mākua ke ole e haawi mai i ka maopopo ia. A ia anei ia mea ina he kumu opiopioʻia trapped ...

Incidentally, ka mea e e hoʻomaopopo i ka luna-i oleloia rula mea mana no ka multiplication, a no ka fission. Ke huahana o ka hopena maikaʻi a me ka maikaʻi nui wale "e haawi aku i ka hua. Inā he mea mau helu a me ka hoailona "-", i ka hopena o ka maikaʻi helu. ʻO ia pili i ka mahele. Inā kekahi o na helu e e io, alaila, o ka puu hapa, e kekahi e me ka hoailona "-".

E wehewehe i ka pono o ke kānāwai o ka makemakika, ia mea pono e formulate i ka axiom apo. Akā, e ike mua i ia mea. I makemakika kapa komo lima 'ia paha ma i nā hana' ole a me nā kumu mua. Akā, e maopopo ia maikaʻi me ka laʻana.

axiom ke komo lima o

Aia i kekahi mau makemakika kānāwai.

• Ka mua o kēia mau commutative, e like me ia, C + V = V + C.
• Ka lua ua kapaia associative (V + C) + D = V + (C + D).

Ka mea, i nonoi aku nei a me ka multiplication (V m C) m D = V m (C m D).

'Aʻohe ua kāpaeʻia a me na rula e i ka hamama māhele (V + C) m D = V m D + C m D, ia mea i oiaio ia C He m (V + D) = C m V + C m D.

A eia hoi, ka mea i loaʻa i ke apo no ka ihu ke komo i ka hana'ākilikai ma ka hou o ka hehee ai, i ka hana o ka a na kēia mau mea oiaio: C + 0 = C. I hou, no kela a me keia e ku pono ana C mea he hehee ai i ke koho hiki like (-C). Pela C + (-C) = 0.

Deducing axioms no ka io helu

? I'āpono i ka luna olelo, he mea hiki ke pane i ka nīnau: "" eia kekahi "i ka" io "haawi kekahi hoailona" ike i ka axiom e pili ana i ka multiplication o ka io nui, e pono e hoomaopopo aku i ka oiaio (-C) m V = - (C m V). A no hoi, ka mea oiaio, ua like me: (- (- C)) = C.

E hana i kēia, mua mākou i e ho'āʻo i kēlā me kēia o nā kumu mua he mea wale nō kekahi e ku pono ana ia ia "hoahanau." E hoomanao i ka mea kēia hoike. E ka ho'āʻo e noonoo ai i na mea o ka C e ku pono ana i mau huahelu - V a me D. Mai keia ka mea, penei i C + V = 0 a me C + D = 0, oa C + V = 0 = C + D. ka hoʻomanaʻoʻana i ka commutative kānāwai, a ma luna o ka waiwai o ka helu 0, ua hiki ke noonoo i ka huina o nā mea a pau ekolu helu: C, V, a me ka ho'āʻo e imi mai i ka waiwai o D. V. kekahi hoʻonohonoho, V = V + 0 = V + (C + D) = V + C + D, mahope mai o ka waiwai io o ka C + D, i aponoia e like me ka mea ma luna, e lākou, 0. Nolaila, V = V + C + D.

Like me, ka auoiaea waiwai, a no D: D = V + C + D = (V + C) + D = 0 + D = D. Mai keia, ka mea i ike i V = D.

I mea e maopopo ke kumu a pau i ka "hua hoʻohui" i "io" haawi i ka "hua", ia mea pono e maopopo i ka eia. Ke'ōlelo mai, no ka mea, he hehee ai (-C) e kue a C (- (- C)), a laila ka mea, e like i kekahi i kekahi.

A laila, ka mea, ua maopopo i 0 m V = (C + (-C)) = C m V m V + (-C) m V. Mai keia ka mea, penei i C m V oppositely (-) C m V, nolaila, (- C) m V = - (C m V).

No ka piha makemakika mea koʻikoʻi ia pono i paa i 0 m V = 0 no kekahi hehee ai. Inā 'oe e hahai i ka ke kūpili, laila 0 m V = (0 + 0) X 0 m V = V + 0 m V. kēia' o ia hoʻi i ka hou ana o ka huina hoonui 0 m V 'aʻole e hoʻololi i ka mea i hoakakaia dala. keia hana a pau ma hope o ka 'Aʻohe.

Ike a pau o kēia mau axioms hiki ke loko ole wale me ka "hua hoʻohui" e "io" haawi, akā, i ua loaa ma ka hoonui io huahelu.

Multiplication a me ka māhele o nā helu a me ka hoailona "-"

Me ka hele ana i loko o ka makemakika nuances, e ke ho'āʻo i simpler ala e wehewehe i ka rula o ka hana me ka io nui.

Kuhi i C - (-V) = D, ma luna o kēia kumu, C = D + (-V), a laila C = D - V. E hoolilo a me ka V, ua ike ia C + V = D. Oia hoi, o ka C + V = C - (-V). Kēia hana wehewehe ke kumu o ka olelo, ma laila nō nā "hua" i loko o ka lalani, i mai la i ka hoailona e e loli no ka "hua hoʻohui". Ano, e ka hana me ka multiplication.

(-C) m (-V) = D, ma ka 'aoʻao o ke hoʻokomo, a unuhi i nā'ālike liilii mea e ole hoʻololi i kona waiwai: (-C) m (-V) + (C m V) - (C m V) = D.

E hoʻomanaʻo mākou i nā rula o ka staple hana, ua loaʻa:

1) (-C) m (-V) + (C m V) + (-C) m V = D;

2) (-C) m ((-V) + V) + C m V = D;

3) (-C) + C m 0 m V = D;

4) C m V = D.

Mai keia ka mea, penei i C m V = (-C) m (-V).

Like me, kekahi ke hoike mai i ka hopena o ka papa o nā hopena maikaʻi 'huahelu, e ikaika.

General makemakika lula

O ka holo ana, ua wehewehe mea i pono no iniiaiie kula keiki poe i pono e hoomaka ana e aʻo Hōʻuluʻulu io helu. Ke Kuahiwi O pono wehewehe ana i ka mea i nanaia e hoopii mai ai, manipulating manawa maʻa iā ia ma ke aniani. No ka laʻana, invented, akā,ʻaʻohe na toys i laila. Ia a hiki ke hōʻike i ka hoailona "-". Multiplication o nā mea transmirror 'ohua' ia i loko o kekahi ao, i mea like me ka makana, i mea, e like me ka hopena, ua i maikaʻi helu. Akā, i ka multiplication o Hōʻuluʻulu io helu i ka maikaʻi haawi wale hualoaʻaʻike i nā mea a pau. Ma hope o nā mea a pau, i ka "hua hoʻohui" hoonuiia e ka "hua" i hāʻawi mai i ka "hua". Naʻe, i loko o ka iniiaiie kula mau makahiki keiki ka mea,ʻaʻoleʻoi aku ana e komo i loko o nā mea a pau o ka makemakika nuances.

Oiai, ina e alo i ka oiaio, no ka nui kanaka, e like me ka hoʻonaʻauao kiʻekiʻe noho i kekahi mea pohihihi nui lula. A pau ia mea no ia i ao aku kumu ia,ʻaʻole keu aku nō pilikia e delve i loko o nā pilikia a pau hoʻomaopop 'ana i loko o ka makemakika. "Noke" i "io" haawi "eia" - a pau ike e pili ana ia, me ka a koe. He like oiaio no ka mea a pau, a no ka fractional loa.