Meej pem xov tooj thiab ua hauj lwm rau lawv

Lub tswvyim ntawm tus xov tooj hais txog cov abstraction uas characterizes ib tug kwv los ntawm ib tug ntau taw tes ntawm view. Tsis tau muaj ib tug yuav tsum tau khiav yam, thiaj li muaj tau hais txog zauv designations nyob rau hauv ib tug txheej thaum ub haiv neeg cov neeg. Tom qab ntawd lawv los ua lub hauv paus ntawm kev kawm txog zauv raws li ib tug science.

Mus leg zauv tswv yim, nws yog tsim nyog, ua ntej ntawm tag nrho cov, xav txog tej yam dab tsi zoo ntawm cov zauv yog. Ob peb lub ntsiab hom ntawm cov zauv. Lawv yog:

1. Ntuj - qhov sawv daws yuav peb tau txais nyob rau hauv lub numbering ntawm cov khoom (lawv tej yam ntuj tso account). Ib tug ntau ntawm lawv sawv cev rau lub Latin tsab ntawv N.

2. Tag nrho cov (lawv set yog denoted los ntawm tsab ntawv Z). Cov no muaj xws natural, opposite rau lawv tsis zoo zauv thiab pes tsawg.

3. Meej pem xov tooj (tsab ntawv Q). Lawv yog cov uas tej zaum yuav muaj tuaj raws li ib feem, lub numerator uas yog sib npaug zos rau ib tug integer, thiab cov denominator - lub ntuj. Tag nrho cov zauv thiab tej yam ntuj tso tus xov tooj yog muaj kuab.

4. Actual (lawv denoted los ntawm tsab ntawv R). Lawv muaj xws li cov kuab thiab irrational xov tooj. Hu ua irrational xov tooj los ntawm muaj kuab muab los ntawm ntau yam hauj lwm (muab xam rau ntawm lub logarithm paus extract), lawv tus kheej yog tsis muaj kuab.

Yog li, ib yam ntawm cov poob lawm yog ib tug subset ntawm cov hauv qab no yog. Piv txwv ntawm no thesis yog ib daim duab nyob rau hauv daim ntawv t. N. Euler voj voog. Daim duab yog ib tug plurality ntawm concentric ovals, txhua tus uas yog nyob rau hauv lub lwm yam. Puab, qhov tsawg tshaj plaws dawb nyob rau hauv loj (cheeb tsam) yog lub teeb ntawm tej yam ntuj tso tus xov tooj. Nws kiag li npog thiab muaj xws li ib cheeb tsam uas symbolizes lub teeb ntawm cov zauv, uas, nyob rau hauv lem, lies tsis pub dhau lub sau ntawm rational numbers. Sab nrauv, loj tshaj oval, muaj tag nrho cov lwm tus neeg, sawv cev rau ib tug array ntawm cov zauv tiag tiag.

Nyob rau hauv no tsab xov xwm peb xav txog lub teeb ntawm rational numbers, lawv lub zog thiab yam ntxwv. Raws li twb tau hais, lawv muaj xws li tag nrho cov uas twb muaj lawm tus xov tooj (zoo li zoo li tsis zoo thiab pes tsawg). Meej pem xov tooj roos ib txhis series muaj raws li nram no cov khoom:

- qhov no set yog kom, uas yog, kev noj tej khub ntawm cov zauv nyob rau hauv no series, peb yuav yeej ib txwm qhia uas lawv yog ntau dua;

- noj tej yam khub ntawm cov zauv, peb yuav yeej ib txwm muab tso rau nruab nrab ntawm lawv tsawg kawg yog ib tug ntau, thiab, thiaj li, ib tug xov tooj ntawm cov neeg - vim li ntawd rational numbers yog ib qho infinite series;

- tag nrho plaub xam ua hauj lwm nyob rau hauv xws xov tooj tej zaum yuav tshwm sim ntawm lawv yog yeej ib txwm muaj tej yam muaj pes tsawg tus (cov rational); nrog rau cov kev zam ntawm kev faib los ntawm 0 (zero) - nws yog tsis yooj yim sua;

- tej rational numbers yuav tuaj raws li decimal fractions. Cov zauv feem tej zaum yuav yog finite los yog infinite periodic.

Los sib piv cov leb yog hais txog lub teeb ntawm muaj kuab, nws yuav tsum tau nco ntsoov hais tias:

- tej zoo xov tooj ntau dua tshaj pes tsawg;

- tej yam tsis zoo pes tsawg yog yeej ib txwm tsawg tshaj li pes tsawg;

- thaum muab piv ob yam tsis zoo rational numbers ntau dua ces ib tug uas nws tsis muaj nuj nqis (modulus) tsawg.

Yuav ua li cas mus ua yeeb yam nrog rational numbers?

Yuav kom quav ob tug zauv nrog ib yam, nws yog tsim nyog los muab lawv cov tsis tseem ceeb thiab muab tso rau hauv pem hauv ntej ntawm lub sum ntawm tag nrho cov cim. Yuav kom ntxiv tus xov tooj nrog txawv tej yam tshwm sim yuav tsum tau ntawm ntau dua tus nqi rho tsawg thiab muab tso rau lub kos npe rau ntawm lawv, nws tsis muaj nuj nqis yog ntau dua.

Rau subtracting ib tug muaj kuab tooj los ntawm lwm txaus xov tooj mus rau thawj ntxiv ob opposite. Rau txawj ob tug zauv uas koj yuav tsum muab cov nqi ntawm lawv tsis muaj nuj nqis. Cov tshwm sim yuav tsum zoo yog hais tias yam yog ib yam, thiab tsis zoo yog tias sib txawv.

Lub division yog ua piv, uas yog, lub meej qhov tseem ceeb yog lwm yam, thiab cov no ua muab tso rau hauv pem hauv ntej ntawm lub kos npe rau "+" nyob rau hauv cov ntaub ntawv ntawm coincidence ntawm cov cim ntawm lub tawn thiab cov divisor, thiab kos npe rau "-" nyob rau hauv cov ntaub ntawv ntawm ib tug mismatch.

Degrees ntawm rational numbers tshwm sim raws li ib tug cov khoom ntawm ntau yam sib npaug zos rau txhua lwm yam.