Sisitimu yeNhamba Chaiyo
Sisitimu yenhamba chaiyo ndeimwe yepfungwa dzakakosha mumasvomhu, inoshandiswa kuratidza huwandu hwese hwatinosangana nahwo muhupenyu hwezuva nezuva, kubva pakureba nehuremu kusvika pakupisa kusvika pakumhanya nenguva. Nhamba chaiyo ndiyo hwaro hwemapazi akasiyana-siyana emasvomhu akadai sealgebra, geometry, calculus, uye statistics, uye ndiwo mutauro mukuru wesainzi neinjiniya. Kunzwisisa sisitimu yenhamba chaiyo kunoreva kunzwisisa kuti nhamba dzinopatsanurwa sei, kuti dzinobatana sei, uye kuti hunhu hwadzo hunotigonesa sei kuita maverengero nemamodheru nguva dzose.
Kunzwisisa Nhamba Chaidzo
Nhamba chaidzo inhamba dzese dzinogona kuiswa pamutsetse wenhamba. Izvi zvinosanganisira nhamba dzakarongeka nedzisina musoro. Zvichitaurwa, nhamba chaidzo dzinosanganisira nhamba dzese dzinogona kuratidzwa se "kukosha" kwehuwandu hunoenderera mberi, semuenzaniso, kureba kwetafura kunogona kuva mita imwe, mita imwe nehafu, kana kunyange mamita 1,414213.
Nhamba dzechokwadi dzinowanzo ratidzwa nechiratidzo №. Nhamba yega yega chaiyo ine nzvimbo yayo yakasiyana pamutsetse wenhamba, ingave iri negative, zero, kana kuti yakanaka.
Kupatsanurwa kweNhamba muSisitimu yeNhamba Chaiyo
Sisitimu chaiyo yenhamba haisi yega. Ikuwedzera kwesisitimu iri nyore yenhamba. Kuti tinzwisise izvi, tinofanira kutarisa kupatsanurwa kwenhamba dzinoiumba.
1. Nhamba dzechisikigo
Nhamba dzechisikigo dzinowanzo ratidzwa nenhamba. Nhamba idzi dzinoshandiswa kuverenga zvinhu uye dzinowanzo sanganisira:
1, 2, 3, 4, 5, …
Mune dzimwe tsananguro, 0 inosanganisirwawo munhamba dzechisikigo, asi mukudzidzira, mutsauko unowanzoitwa pakati penhamba dzakazara nenhamba dzechisikigo.
2. Nhamba Dzese
Nhamba dzese dzinosanganisira nhamba dzechisikigo pamwe ne zero:
0, 1, 2, 3, 4, …
Nhamba dzakazara dzinobatsira kana tichifanira kutaura kuti “hapana chinhu” (zero) mukuverenga.
3. Nhamba dzese
Nhamba dzese dzinoratidzwa nenhamba ℤ uye dzinosanganisira nhamba dzese nenhamba dzisina kunaka:
…, −3, −2, −1, 0, 1, 2, 3, …
Nhamba dzese dzakakosha pakuratidza mamiriro ezvinhu ane chekuita nemirairo kana kukosha "pasi pe zero," senge tembiricha dziri pasi pechando, chikwereti, kana kukwirira kuri pasi pegungwa.
4. Nhamba Dzepfungwa
Nhamba dzinonzwisisika dzinoratidzwa nenhamba ℚ. Nhamba iyi inhamba inogona kunyorwa muchimiro chezvikamu:
\[
\frac{p}{q}
\]
ne \(p\) uye \(q\) nhamba dzese, uye \(q \neq 0\).
Mienzaniso yenhamba dzinonzwisisika:
– \(\frac{1}{2} = 0,5\)
– \(\frac{3}{4} = 0,75\)
– \(-\frac{7}{5} = -1,4\)
– 2 inogona kunyorwa se \(\frac{2}{1}\)
Hunhu hwakakosha hwenhamba dzepfungwa ndehwekuti chimiro chadzo chedesimali chinoguma kana kudzokorora. Semuenzaniso:
- 0,25 kumira
– 0,333… kudzokorora
5. Nhamba Dzisingakoshi
Nhamba dzisina musoro inhamba chaidzo dzisingagone kuratidzwa muchimiro \(\frac{p}{q}\) apo \(p\) uye \(q\) ari nhamba dzese. Chimiro chedesimali hachimire uye hachidzokorori.
Mienzaniso yenhamba dzisina musoro:
– \(\sqrt{2} = 1,41421356…\)
– \(\pi = 3,14159265…\)
– \(e = 2,7182818…\)
Nhamba dzisina musoro dzinowanzoonekwa mu geometry (semuenzaniso, mudzi wechikwere we diagonal) uye mukuongorora kwemasvomhu.
6. Nhamba Chaidzo
Nhamba chaidzo musanganiswa wenhamba dzakarongeka nedzisina musoro:
\[
\mathbb{R} = \mathbb{Q} \cup (\text{irrational})
\]
Nemamwe mashoko, nhamba dzese dzinogona kumiririrwa pamutsetse wenhamba inhamba chaidzo.
Mutsetse weNhamba uye Pfungwa yeKuwanda kweVanhu
Imwe yenzira dzakanakisisa dzekunzwisisa nhamba chaidzo ndeyekushandisa mutsetse wenhamba. Pamutsetse uyu, poindi imwe neimwe inomiririra nhamba chaiyo. Zvinofadza kuti, pakati penhamba mbiri chaidzo, pane imwe nhamba chaiyo nguva dzose. Semuenzaniso, pakati pa1 na2 i1,5; pakati pa1,5 na2 i1,75; zvichingodaro zvisingaperi.
Hunhu uhwu hunozivikanwa sehuwandu hwevanhu. Manhamba akarongeka neasina musoro akafanana pamutsetse wenhamba: pakati pemanhamba maviri chaiwo, pane nhamba dzakarongeka dzakawanda dzisingaperi uye nhamba dzisina musoro dzisingaperi.
Mashandiro Ekutanga Panhamba Dzechokwadi
Nhamba chaidzo dzinotsigira mashandiro ekutanga emasvomhu anotevera:
1. Kuwedzera: \(a + b\)
2. Kubvisa: \(a – b\)
3. Kuwanza: \(a \times b\)
4. Kupatsanura: \(a \div b\), nechimiro \(b \neq 0\)
Mabasa aya ane zvinhu zvakakosha zvakaita se:
– Kutaurirana: \(a + b = b + a\), \(ab = ba\)
– Mubatanidzwa: \((a + b) + c = a + (b + c)\)
– Kugovera: \(a(b + c) = ab + ac\)
– Ine hunhu: 0 yekuwedzera, 1 yekuwedzera
– Ine inverse: \(-a\) yekuwedzera, \(\frac{1}{a}\) yekuwedzera (ye \(a \neq 0\))
Hunhu uhwu hunoita kuti nhamba chaidzo dzigadzikane senzira yekuverenga.
Kurongeka uye Kukosha Kwakazara
Nhamba chaidzo dzine hukama hwekurongeka. Tinogona kuenzanisa nhamba mbiri chaidzo nechiratidzo chinotevera:
– \(<\) idiki - \(>\) yakakura
– \(\le\) ishoma pane kana kuti yakaenzana ne
– \(\ge\) yakakura kupfuura kana kuti yakaenzana ne
Pamusoro pezvo, pane pfungwa ye absolute value iyo inotaura daro renhamba kubva pa zero:
\[
|a| =
\kutanga{zviitiko}
a, & \text{if} a \ge 0 \\
-a, & \text{if } a < 0 \end{cases} \] Semuenzaniso, \(|-5| = 5\) uye \(|3| = 3\).
