Tsim, Science
Yuav ua li cas yog lub rational numbers? Yuav ua li cas yog qhov ntau?
Yuav ua li cas yog lub rational numbers? Senior tub kawm ntawv thiab tub kawm ntawv ntawm zauv specialties yog yuav mus tau yooj yim teb lo lus nug no. Tab sis cov neeg uas los ntawm txoj hauj lwm yog nyob deb ntawm no, nws yuav nyuab me ntsis. Yuav ua li cas nws yeej yog?
Lub essence thiab los
Nyob rau hauv rational numbers txhais li cas cov neeg uas yuav tsum tau tuaj raws li ib qho feem. Zoo, zoo, thiab pes tsawg kuj muaj nyob rau hauv no set. Lub numerator ntawm lub feem nyob rau hauv cov ntaub ntawv no yuav tsum muaj ib integer, thiab cov denominator - sawv cev rau ib tug zoo integer.
Cov teeb no ntawm kev kawm txog zauv yog raug xa mus rau raws li Q thiab yog hu ua tus "teb ntawm rational numbers." Lawv muaj xws li tag nrho cov tag nrho thiab tej yam ntuj tso, denoted li Z thiab N. Tus heev tib yam txheej Q muaj nyob rau hauv lub teeb R. Nws yog tsab ntawv no sawv cev rau lub thiaj li hu ua tiag tiag los yog cov zauv tiag tiag.
lub tswv yim
Raws li twb tau hais, lub rational numbers - qhov no set, uas muaj xws li tag nrho cov integer thiab fractional qhov tseem ceeb. Lawv yuav tsum tau nthuav tawm nyob rau hauv ntau yam ntaub ntawv. Firstly, nyob rau hauv daim ntawv ntawm cov zoo tib yam fractions: 5/7, 1/5, 11/15, lwm yam Ntawm cov hoob kawm, tus zauv tej zaum kuj yuav sau nyob rau hauv ib txoj kev zoo: 6/2, 15/5, 0/1, - .. 10/2, etc. ob txhais, lwm hom kev nthuav qhia - ib tug finite decimal fractional ib feem: .... 0.01, -15,001006, thiab lwm yam no yog tej zaum ib tug ntawm feem ntau cov ntaub ntawv.
Tab sis muaj ib tug thib peb - periodic feem. Cov hom yog tsis heev, tab sis tseem siv tau. Piv txwv li, lub feem 10/3 yuav sau raws li 3,33333 ... los yog 3, (3). Lub sib txawv views yuav muab suav hais tias tib tus. Raws li yuav tsum tau xa mus rau, thiab sib npaug zos rau txhua lwm yam fractions xws li 3/5 thiab 6/10. Nws nkawd hais tias nws muaj tseeb hais tias ib tug muaj kuab tooj. Tab sis yog vim li cas yog lub sij hawm siv los xa mus rau lawv?
Keeb kwm ntawm lub npe
Lo lus "muaj kuab" nyob rau hauv lub niaj hnub Lavxias teb sab lus nyob rau hauv kev yog ib tug me ntsis txawv ntsiab lus. Tiamsis, nws yog "tsim nyog", "txhob txwm". Tab sis xyuam xim cov ntsiab lus uas yog nyob ze rau hauv lub literal siab ntawm lub borrowed lo lus. Lub "piv" nyob rau hauv Latin - yog "tus cwj pwm", "yob" los yog "faib." Yog li, lub npe no qhia lub essence ntawm dab tsi yog muaj kuab. Txawm li cas los, qhov thib ob lub ntsiab lus
manipulating
Nyob rau hauv kev daws xyuam xim teeb meem, peb tas li confronted nrog rational numbers, tsis paub lawv tus kheej ua. Thiab lawv muaj ib tug xov tooj uas interesting lub zog. lawv tag nrho cov ua raws li los ntawm lub ntsiab txhais ntawm ib co ntawm cov kev ua yog.
Ua ntej, cov rational numbers muaj cov cuab yeej kev sib raug zoo ntawm qhov kev txiav txim. Qhov no txhais tau tias ntawm ob tus xov tooj yuav ua tau tsuas yog ib tug kev sib raug zoo - lawv yog tog twg los sib npaug zos rau txhua lwm yam, los yog ib tug ntau dua los yog tsawg tshaj li lwm tus. Xws li.:
los yog ib tug = b; los yog ib tug> b, los yog ib tug
Tsis tas li ntawd, cov cuab yeej no ntawm transitivity piv raws li nram no. Uas yog, yog tias ib tug yog ntau tshaj b, b ntau tshaj c, ces ib tug yog ntau tshaj c. Nyob rau hauv cov lus ntawm kev kawm txog zauv yog raws li nram no:
(A> b) ^ (b > c) => (a> c).
Secondly, muaj xam hauj lwm nrog rational numbers, piv txwv li, tsis tas li ntawd, kev rho tawm, division, thiab, ntawm chav kawm, kev ua lej khu. Nyob rau hauv tus txheej txheem ntawm transformation yuav tau xaiv ib tug xov tooj ntawm cov khoom.
- ib tug + b = b + ib (hloov cov nqe lus qhov chaw commutativity);
- 0 + a = ib tug + 0;
- (A + b) + c = ib tug + (b + c) ( associativity);
- ib tug + (piv) = 0;
- ab = kav ywm;
- (B) c = ib (bc ) ( Distributivity);
- 1 = taus 1 Xa = ib;
- taus (1 / a) = 1 (nyob rau ib yog tsis 0);
- (A + b) c = ac + ab;
- (A> b) ^ (c > 0) => (ac> bc) .
Thaum nws los txog rau tib yam, tsis zauv, fractions thiab zauv, kev ua nrog lawv tej zaum yuav ua rau ib co teeb meem. Piv txwv li, ntxiv thiab rho tsuas yog tau nrog sib npaug denominators. Yog hais tias lawv yog cov sib txawv chiv, yuav tsum tau mus nrhiav tau ib tug ntau, siv ib tug npaug ntawm tag nrho cov zauv feem rau ib tug tej yam muaj pes tsawg tus. Piv feem ntau kuj tsuas tau nyob rau hauv tus mob no.
Cov kev faib thiab npaug ntawm cov zauv feem nyob rau hauv raws li haum kev cai yooj yim. Lub txo mus rau ib tug ntau denominator yog tsis tsim nyog. Nyias, muab lub numerators thiab denominators, thaum nyob rau hauv tus txheej txheem ntawm kev siv ntawm cov feem tau kev ua yuav tsum tau mus txo thiab piv.
Raws li rau lub division, ces nws yog zoo li mus rau tus thawj nrog ib tug me ntsis txawv. Rau qhov thib ob txhaj koob tshuaj tivthaiv yuav tsum nrhiav tau cov rov qab, uas yog,
Thaum kawg, lwm cov vaj tse qhia los ntawm rational numbers, hu ua lub axiom ntawm Archimedes. lub npe ntawm lub "hauv paus ntsiab lus" yog feem ntau pom nyob rau hauv cov ntawv nyeem thiab. Nws yog siv tau rau tag nrho cov txheej ntawm cov zauv tiag tiag, tiam sis tsis qhov txhia chaw. Yog li, txoj ntsiab cai no tsis siv rau tej yam poob lawm ntawm muaj kuab zog. Nyob rau hauv essence, qhov no axiom txhais tau tias thaum muaj ob qhov tseem ceeb ntawm ib tug thiab b, koj yeej ib txwm coj ib tug txaus tus nqi ntawm ib tug, b rau outperform.
kheej ntawm daim ntawv thov
Yog li ntawd, cov neeg uas yog kawm los yog nco qab txog, hais tias ib tug muaj kuab tooj, nws yog ib qhov tseeb hais tias lawv yog siv qhov txhia chaw: nyob rau hauv accounting, economics, statistics, physics, Science News for KIDS thiab lwm yam sciences. Lawm, muaj kuj yog qhov chaw rau lawv nyob rau hauv kev kawm lej. Tsis yeej ib txwm paub tias peb yuav soj ntsuam nrog lawv, peb tas li siv rational numbers. Txawm cov me nyuam me kawm rau suav khoom, txiav mus rau hauv qhov chaw kua los yog ua kom tiav lwm yam yeeb yam yooj yim, kev nyuaj siab nrog lawv. Lawv cia koos peb. Txawm yog tej yam kev pab raws qib lawv yog tsis txaus, nyob rau hauv particular, tus yam ntxwv ntawm lub Pythagorean theorem, peb yuav to taub qhov xav tau ntawm plaug lub tswvyim ntawm irrational xov tooj.
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