Ka hana mau

'O ka hana ma'amau he hana me ka'ole "pīpī",'o ia ho'i, kahi no ka ho'opiha'ia'ana o ke kūlana:'o nā loli li'ili'i o ka pane ke ukali'ia e nā loli li'ili'i i nā helu like o ka hana. 'O ka pakuhi o ia'ano hana he kemu lemu a ho'omau paha.

Hiki ke ho'omau i ke ka'ina ma kahi pāna'i e hiki ke ho'oholo i ka palena no kekahi ho'onohonoho ma ka ho'ohana'ana i ke kumumana'o o ka palena,'o ia ho'i: pono ka hana i kahi palena ma kēia wahi,'o ia ke kūlike i kona kūlana ma ka palena palena.

Inā hō'ino'ia kēia mau mea i kekahi manawa, ua'ōlelo'ia ua kaumaha ka hana ma kekahi mahele i hā'awi'ia,'o ia ho'i, ua uha'i'ia kona mau holomua. Ma ka'ōlelo o nā palena, hiki ke wehewehe'ia ka helu o ka ho'opau'ana e like me ka hō'ailona o ka waiwai o kahi hana ma kahi pau'ole me ka palena o kahi hana (inā he mea ia).

Hiki ke ho'opau'ia ke kumu o ka ho'omaha, no ka mea, he mea pono e loa'a ka palena o kahi hana, akā,'a'ole ia e kūlike i kona waiwai ma kahi i hā'awi'ia. I kēia hihia, hiki ke "ho'oponopono" i kēia wahi,'o ia ho'i, hiki ke ho'onui i ka holomua.
A pau loa ia kekahi kiʻi mńlie ina o ka palena o ka papa ma ka hāʻawi wahi, aole ia e nei. Elua mau kumu like'ole o nā ha'alulu:

• 'O ka'ano mua - e kū ana nā'ao'ao'elua o nā'ao'ao a ua pa'a, a'o ka waiwai o kekahi o lākou a'elua paha,'a'ole ia e kūlike me ka waiwai o ka hana ma kahi i hā'awi'ia;
• 'O ka lua o nā'ano, i ka manawa e'ole ai ho'okahi a'elua paha o nā palena palena'ole a'a'ole loa e pau ko lākou mau waiwai.

Nā hana o nā hana mau

• 'O ka hana i loa'a ma ka hopena o nā hana helu helu, a me ka ho'omau'ana i nā hana mau i ko lākou mau wehewehe'āina, e ho'omau'ia ana.
• Inā hā'awi'ia kahi hana mau e kūpono ma kekahi wahi, a laila, hiki i kekahi ke'imi i kahi kaiāulu li'ili'i e pili ana i laila, kahi e pa'a ai i kona hō'ailona.
• Pēlā like, inā kū like kona mau helu ma nā helu'elua A a me B, i kēlā me kēia, a a me b, me kahi'ē a'e o ka b, a laila no nā wahi waena e lawe i nā waiwai a pau mai ka wā (a, b). Mai kēia wahi e hiki iā mākou ke huki i ka hopena maika'i: inā e hā'awi mākou i ka pā kau e ho'opili'ia i'ole e lag (kū pololei), a laila e pa'a kekahi o kona mau kiko. A o geometrically, eia ke'ano o ka laina ma'amau e hele ana ma waena o ka manawa waena ma waena o A a me B, kahi e kuhi ana i ka pakuhi o ka hana.

Ke'ike nei mākou i kekahi o ka mau e ho'omau (ma ka mana o ko lākou wehewehe) mau lawelawe ha'aha'a:

• Ho'omau;
• Rational;
• 'O ke kaha.

Ma waena o nā kumumana'o nui'elua i ka makemakika - ka holomua a me ke ka'awale'ana - aia kahi link inextricable. 'A'ole pono e ho'omana'o i ka mea e pono ai ka hana'ana he pono ke hana mau.

Akā, inā he'oko'a ka hana ma kekahi wahi, a laila ua mau. Akā na'e,'a'ole kūpono e ho'omau'ia kāna huahana.

'O kahi hana e hele mau ana ma kahi ho'onohonoho ho'okahi, he'ano o nā'oihana maika'i. I nā hua'ōlelo'ē a'e, he hana keakea mau kēia. Inā he helu ka palena o nā huahāhā ('o kahi wale nō ke'ano), a laila, ua'ōlelo'ia kekahi hana like e like me ka li'ili'i.

ʻO kekahi mea nui manaʻo o ka makemakika Ka Ikepili mea uniformly ana hana, i mea, kona hiki ia ia ma kekahi wahi o kona kikowaena o ka ia ana. No laila, ua mana'o'ia kēia waiwai ma nā wae helu,'a'ole i loko o kēlā me kēia mea i ho'oka'awale'ia.

Inā mākou e ho'oponopono i ka helu,'a'ole mākou e loa'a ka mea'ē a'e ma ka ho'ākāka'ana o ka holomua,'o ia ho'i,'o ka noho mau'ana o ka papahana e hō'ike ana he hana mau kā mākou. 'O ka'ōlelo ma'amau,'a'ole pono ka'ōlelo. Eia na'e, e like me ka'ōlelo a Cantor, inā he hana mau ka hana ma kahi compactum,'o ia ho'i, ma kahi ākea, a laila e kau mau'ia ma laila.