Ho okumu, 'epekema
He aha ka ka naauao helu? He aha e ka mea hou?
He aha ka ka naauao helu? Pāhana haumana nā haumāna o ka makemakika meaʻai poʻokela pepa, a mea paha e hiki wawe ka pane i kēia nīnau. Akā,ʻo ka poʻe ma kaʻoihana mea mamao aku, mai keia, ka mea, e ia ka paʻakikī. He aha ia nae mea?
Ke o Mānoa, a me ka inoa
Ma lalo o ka naauao helu olelo nei au no ka poe i hiki ke poe me ka hoʻomaopopo like hapa. 'Oluʻolu, io, a me ka' Aʻohe mea i komo i loko o kēia 'ia paha. pono ia i helu i ka numerator o ka mahele i loko o keia hihia, a me ka denominator - ho i ka maikaʻi helu.
Kēia poʻe o ka makemakika ua haawi ia ia e like me Q, a ua kapaia o ka "aina o ka naauao loa." Ka mea, nā mea a pau a pau, a ma kona ano maoli, denoted me Z a me N. ka loa e like me kau o Q me ia ma ka huapalapala R. It mea keia palapala ho i ka ai-kapaia maoli a me maoli helu.
manaʻo
E like me ua oleloia, o ka ka naauao helu - keia kau, i nā mea a pau i ka helu a me ka fractional nā loina. Ka mea hiki ke hooku iho la ia ia ma kekahi 'ano apau loa. Mua, i loko o ka palapala o ke ano o mahele: 5/7, 1/5, 11/15, etc. Of papa, na integers hiki i ke kākau i loko o ka like alanui: 6/2, 15/5, 0/1, - .. 10/2, etc. elua, kekahi 'ano o ka hōʻike - he finite kekimala fractional hapa: .... 0,01, -15,001006, etc. kēia mea paha i kekahi o ka loa, he pono ole pepa.
Akā, he mea i ke kolu - papa'āweʻaweʻa kemika mahele. Kēia? Ueo mea ole loa, he pono ole, akā nō i hoʻohana. No ka laʻana, i ka mahele 10/3 hiki ke kākau like 3,33333 ... a me 3, (3). e ke kekahi mau manao e noʻonoʻo i ka ia helu. Like e e haawiia ia, a me ka ewaewa ole i kekahi i kekahi hapa e like me 3/5 a me 6/10. Pēlā ka manaʻo o ka mea, ua lilo ia i mea akaka i ka naauao helu. Akā, no ke aha la e ke kau hoʻohana 'ia e hoʻohuli i ia ia?
Kumu o ka inoa
Ka hua'ōlelo "naauao" i loko o ka kēia Lūkini 'ōlelo i loko o kekahi mau hāpai ka iki okoa manaʻo. Kaupalena naʻe, ka mea, o "kumu", "deliberate". Akā, makemakika hua'ōlelo e kokoke ana i ka literal ano o ka aie olelo. Ka "hiʻohiʻona" ma Roma - ka "heluia, e", "owili" a me "ke ku e." Ke'ī mai, i ka inoa Hōʻike 'o ka pā o ka mea naauao. Naʻe, i ka lua o ka manaʻo
Manipulating
Ma ka hoʻoponopono makemakika pilikia, ua i mau alo me ka naauao nui, i ka ike ana ia lakou iho hana. A ka mea, i ka helu o ka hoihoi 'waiwai. ka mea, a pau e hahai mai i ka wehewehena o ka lākou o nā hana kekahi.
Mua, o ka ka naauao helu i ka waiwai ana o ka mea. Kēia 'o ia hoʻi i waena o nā helu elua hoʻokahi wale nō pilina hiki e - ka mea, i kekahi like i kekahi i kekahi, a me kekahi oi a emi ma mua o kekahi. Ie.:
a he = b.; a he> e, a me ka
Eia kekahi, keia waiwai o ka transitivity hiʻohiʻona like penei. Ia mea, ina o ka mea i oi aku mamua e, e oi ma mua o pela aku, alaila, he mea oi aku ia mamua c. Ma ka 'ōlelo o ka makemakika, ua like penei:
(He> b) '(b > c) => (i> c).
Ka lua, eia makemakika ana me ka naauao nui, 'o ia hoʻi, hou, subtraction, mahele, a, o ka papa, multiplication. Ma ke kaʻina hana o ka hou 'hiki i koho i ka helu o ka waiwai.
- he + a b = e + i ka (loli hua'ōlelo wahi commutativity);
- 0 + i = i + 0;
- (He + b) + pela aku = i + (b + c) ( associativity);
- He + (-a) = 0;
- ab = BA;
- (Ab) c. = I (BC ) ( Distributivity);
- 1 = koʻi 1 xa = i;
- koʻi (1 / i) = 1 (kahi i kekahi mea,ʻaʻole 0);
- (He + b) l = AC + ab;
- (He> b) ^ (c > 0) => (AC> BC) .
I ka wa e hele mai i ka maʻamau,ʻaʻole kekimala, mahele a me integers, hana me ia e i kekahi pilikia. No ka laʻana, e hiki wale hou a me ka subtraction me ka like denominators. Inā ka mea, e okoa initially, e lilo ia i loaʻa i kekahi, he pono ole, ka hoʻohana 'ana i ka multiplication o nā mahele ma luna o kekahi o kekahi helu. Hoʻohālikelike hoi pinepine wale nō e hiki ma lalo o keia kulana.
Mahele a me ka multiplication o ka hapa hua mai la ia e like me ke 'ano mea lula. Ke ka ho'ēmiʻana i ka nui denominator mea i pono. Kaawale, e hoonui i ka numerators a me denominators, oiai i loko o ke kaʻina hana o ka manaʻo o ka mahele hiki hana pono e kń a Nohie.
Like no ka mahele, alaila, ia mea i 'ano like me ka mea mua a me ka hōʻemi iki like. No ka mea lua o ka pana pono i loaʻa i ka inverse, ia mea,
Eia hoi, kekahi waiwai kaʻana 'ia e ka naauao nui, i kapaʻia ka axiom o Archimedes. i ka inoa o ka "rula" ua pinepine i loaʻa i loko o ka moʻokalaleo kekahi. He henua pololei no ka mea holoʻokoʻa kau o maoli helu, akā,ʻaʻole na wahi a pau. Penei, keia rula, aole ia e pili i kekahi e puhi ia o ka naauao i hana '. Ma o Mānoa, keia axiom 'o ia hoʻi i ka wā i loaʻa i nā cia o ka a me ka b, e hiki mau lawe i lawa ka nui o kekahi, e, e outperform.
poepoe o ka palapala noi
No laila, ka poe hoomanao i i aoia ai, i ka naauao helu, ka mea, ua ike i ka mea i hoʻohana wahi: ma ka helu mahina,? Aneia iainiiaaiea, 'ikepili helu, ke kālaikūlohea, kemika a me nā sciences. Maoli ai, he mea no hoi i ka wahi ia ia me ka makemakika. 'Aʻole i mau ka ike ana mākou i ana me ia, ua mau ka naauao helu hoʻohana. O uuku na keiki ke aʻo 'ana i ka helu mea, a oki i hapa kii onohi a hoʻopau' ē aʻe na mea hana,ʻalo me ia. Lakou literally puni mākou. Aka, no kekahi mau hana ka mea, ua lawa, i loko o 'ana, ke kumu hoohalike o ke Pythagorean theorem, ua hiki ke maopopo ka pono o ka manaʻo i hoʻolaunaʻia ma o irrational helu.
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