Koj puas paub tias dab tsi nws txhais tau hais tias "muaj kuab" thiab dab tsi tus xov tooj yog hu ua kuab?

Nyob rau hauv lub deb yav tag los, thaum muaj invented calculus system, tag nrho cov neeg suav rau tus ntiv tes. Nrog lub advent ntawm xam thiab lej nws tau ua ntau yooj yim dua thiab ntau tswv yim kom cov ntaub ntawv los ntawm cov khoom, cov khoom, thiab tsev neeg cov khoom. Txawm li cas los, nws zoo li ib tug niaj hnub system ntawm xam: hom yog muab faib mus rau hauv lub uas twb muaj lawm pes tsawg tus, thiab nws txhais tau tias "ib tug muaj kuab zoo ntawm cov zauv?" Wb fim nws.

Yuav ua li cas ntau ntau yam ntawm tus xov tooj muaj nyob rau hauv kev kawm txog zauv?

Tus heev tswvyim ntawm "xov tooj" hais txog ib tug tej yam unit ntawm ib yam khoom, uas characterizes nws ntau, comparative los yog ordinal ntsuas. Nyob rau hauv thiaj li yuav zoo xam tus naj npawb ntawm kev cov khoom los yog ua zauv hauj lwm nrog cov zauv (daim ntau quav tso multiply li al.), Nyob rau hauv thawj qhov chaw yuav tsum paub txog cov tsiaj rau cov zauv.

Yog li, muaj tshwm sim ib tug xov tooj yuav tsum tau muab faib mus rau hauv lub nram no:

1. Ntuj - cov no yog cov xov tooj peb yuav suav cov xov tooj ntawm cov khoom (.. Lub kawg zoo integer sib npaug zos rau 1, nws yog ib zajlus kom tias ib tug xov tooj ntawm tej yam ntuj tso tus xov tooj yog infinite, piv txwv li, muaj yog tsis muaj loj tshaj tej yam ntuj tso tooj). Txheej ntuj tooj feem ntau yog denoted los ntawm tsab ntawv N.
2. Zauv. Rau no set muaj xws li tag nrho cov natural tooj, thaum nws ntxiv kom zoo qhov tseem ceeb, nrog rau cov xov tooj "zero". Los ntawm lub teeb ntawm cov zauv yog kaw li lub Latin tsab ntawv Z.
3. Meej pem xov tooj - qhov sawv daws yuav hais tias peb yuav muaj kev ntxhov siab hloov mus rau ib feem, lub numerator uas yuav mus rau lub teeb ntawm cov zauv, thiab cov denominator - tej yam ntuj tso. Cia li hauv qab no peb sib tham txog nyob rau hauv ntau yam dab tsi nws txhais tau hais tias "muaj kuab tus xov tooj", thiab muab ib co piv txwv.
4. Cov zauv tiag tiag - set, uas muaj xws li tag nrho cov muaj kuab thiab irrational xov tooj. Cov teeb no yog denoted los ntawm tsab ntawv R.
5. Complex xov tooj muaj ib tug ib feem ntawm ib tug tiag tiag ib feem thiab ib tug nce mus nce los tooj. Siv lej nyob rau txawv nyhav sib npaug, uas nyob rau hauv lem yuav nyob rau hauv cov qauv nyob rau hauv lub hauv paus kos npe rau yog tsis zoo qhia (i ² = -1).

Yuav ua li cas koj txhais hais tias "muaj kuab": rho cov piv txwv

Yog hais tias rational numbers no yog cov uas peb yuav nthuav nyob rau hauv daim ntawv ntawm ib tug ntau feem, nws hloov tawm hais tias tag nrho cov zoo thiab tsis zoo zauv kuj muaj nyob rau hauv lub teeb ntawm muaj kuab. Tseeb, tej integer, xws li 3 los yog 15, tej zaum yuav muaj tuaj raws li ib feem nyob qhov twg cov denominator yuav unit.

Cov zauv: -9/3; 7/5, 6/55 - yog cov piv txwv ntawm rational numbers.

Dab tsi "muaj kuab qhia"?

Mus tom ntej. Peb twb sib tham yog dab tsi nws txhais tau hais tias ib tug muaj kuab saib ntawm lub xov tooj. Cia peb tam sim no xav txog tej yam ib tug zauv qhia, uas muaj tus lej, qhov txawv, cov khoom, los yog ntau yam private tooj thiab zog. Ntawm no yog ib qho piv txwv: ib feem, lub numerator uas yog lub sum ntawm ob los yog ntau tshaj cov zauv, thiab cov denominator muaj xws li ob qho tib si integer thiab ib co nce mus nce los. Nws yog qhov no qhia yog hu ua kuab. Raws li cov kev cai "yuav tsis faib los ntawm xoom" koj yuav twv hais tias tus nqi ntawm no nce mus nce los yuav tsis tsum xws li tias tus nqi ntawm cov denominator vanishes. Yog li ntawd, nyob rau hauv kev soj ntsuam txog nrog ib tug muaj kuab qhia, koj yuav tsum xub txhais tau lub Scope ntawm lub nce mus nce los nqis. Piv txwv li, yog hais tias tus denominator ntawm cov hauv qab no qhia: x + 5-2, nws hloov tawm hais tias "x" tej zaum yuav tsis sib npaug zos rau -3. Tseeb, nyob rau hauv cov ntaub ntawv no, tag nrho cov kev qhia yuav pes tsawg, txawm li cas los nyob rau hauv lub tshuaj yuav tsum muab deleted -3 integer rau ib tug muab nce mus nce los.

Yuav ua li cas los daws kom tau kuab sib npaug?

Rational expressions yuav muaj ib tug ncaj loj npaum li cas ntawm cov zauv los yog txawm 2 variables, li ntawd, tej zaum lawv kev txiav txim siab yuav tsis yooj yim. Yuav kom pab txhawb kev daws ntawm xws ib qho kev qhia yog pom zoo rau tej yam hauj lwm nyob rau hauv ib tug muaj kuab txoj kev. Yog li ntawd, dab tsi "muaj kuab txoj kev" thiab dab tsi cov kev cai yuav tsum muaj ntaub ntawv nyob cov tshuaj?

1. Tus thawj hom, thaum tsuas tau mus piv rau cov kev qhia. Rau lub lag luam no yuav chaw uasi mus rau txo lub numerator thiab denominator rau irreducible nqi. Piv txwv li, yog hais tias muaj yog ib qho kev qhia nyob rau hauv lub numerator ntawm 18x, 9 X thiab cov denominator, ces, txo ob ntsuas rau 9 X, tau ib tug integer ntawm 2.
2. Qhov thib ob hom yog cov tswv yim thaum lub numerator muaj monomial, thiab cov denominator - lub polynomial. Cia peb xav txog ib qho piv txwv: tus numerator muaj 5x, thiab cov denominator - 5x + 20 x ^2. Nyob rau hauv cov ntaub ntawv no, nws yog ib qhov zoo tshaj plaws los mus ua kom ib tug nce mus nce los nyob rau hauv lub denominator ntawm lub nkhaus, peb muab tau cov nram qab no daim ntawv ntawm lub denominator: 5x (1 + 4 x). Thiab tam sim no koj muaj peev xwm siv cov thawj txoj cai thiab piv cov kev qhia, kom txhob muaj cov 5x nyob rau hauv lub numerator thiab denominator lub. Raws li ib tug tshwm sim, peb muab tau cov feem ntawm daim ntawv 1/1 + 4 x.

Yuav ua li cas yuav ua li cas nrog rational numbers?

Lub teeb ntawm rational numbers muaj ib tug xov tooj ntawm cov nta. Muaj ntau ntawm lawv yog cov zoo heev rau ib tug yam ntxwv tam sim no nyob rau hauv tag nrho thiab tej yam ntuj tso tus xov tooj, vim lub fact tias cov tom kawg yog yeej ib txwm muaj nyob rau hauv lub teeb ntawm muaj kuab. Ntawm no yog ib co yam ntxwv ntawm rational numbers, paub txog tias koj yuav yooj yim kom daws tau tej kuab qhia.

1. commutative vaj tse enables koj los ntsuas ob los yog ntau tshaj tus xov tooj, tsis hais ntawm lawv cov ua ntej. Cias muab, nyob rau cov nyaj ntawm sum yog tsis tau hloov.
2. lub distributive vaj tse tso cai rau peb kom daws tau qhov teeb meem siv cov distributive kev cai lij choj.
3. Thaum kawg, ntxiv thiab rho.

Txawm schoolchildren paub dab tsi nws txhais tau tias "ib tug muaj kuab saib ntawm lub xov tooj" thiab yuav ua li cas los daws kom tau teeb meem nyob rau hauv lub hauv paus ntawm tej kab zauv, yog li ib tug neeg laus kawm ntawv tus neeg tsuas xav tau kom rov qab tsawg kawg yog tsim ntawm lub teeb ntawm rational numbers.