Ƙarin juyawa

opposite number

A cikin ilimin lissafi, additive inverse na wani element x, wanda ake nunawa -x , shine sinadarin da idan aka saka shi zuwa x, yana haifar da ma'anar ƙari, 0 . A cikin al'amuran da aka fi sani, wannan ita ce lamba 0, amma kuma tana iya komawa zuwa mafi yawan sifili .

A cikin ilimin lissafi na farko, ana kiran ƙari inverse a matsayin kishiyar lamba . Tunanin yana da alaƙa kusa da raguwa kuma yana da mahimmanci wajen warware ma'auni na algebra . Ba duk saitin da aka ayyana ƙari yana da ƙari ba, kamar lambobi na halitta .

Misalai gama gari

Lokacin aiki da lambobi, lambobi masu ma'ana, lambobi na ainihi, da lambobi masu rikitarwa, ana iya samun juzu'i na kowane lamba ta ninka ta -1 .

Waɗannan lambobi masu rikitarwa, biyu daga cikin ƙima guda takwas na 8 √ 1, suna gaba da juna

Sauƙaƙan Halin Ƙarfafa Ƙarfafawa

$n$	$-n$
$7$	$-7$
$0.35$	$-0.35$
$\frac{1}{4}$	$-\frac{1}{4}$
$\pi$	$-\pi$
$1+2i$	$-1-2i$

Hakanan za'a iya ƙaddamar da ra'ayi zuwa maganganun algebra, wanda galibi ana amfani dashi lokacin daidaita daidaito .

Ƙarin Inverses na Maganar Algebraic

$n$	$-n$
$a-b$	$-(a-b)=-a+b$
$2x^2+5$	<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mo>$-(2\mathrm{x}{\phantom{A}}^2+5)=-2\mathrm{x}{\phantom{A}}^2-5$</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false"> $-(2\mathrm{x}{\phantom{A}}^2+5)=-2\mathrm{x}{\phantom{A}}^2-5$</mo><mn> $-(2\mathrm{x}{\phantom{A}}^2+5)=-2\mathrm{x}{\phantom{A}}^2-5$</mn><msup><mtext> $-(2\mathrm{x}{\phantom{A}}^2+5)=-2\mathrm{x}{\phantom{A}}^2-5$</mtext><mrow class="MJX-TeXAtom-ORD"><mn> $-(2\mathrm{x}{\phantom{A}}^2+5)=-2\mathrm{x}{\phantom{A}}^2-5$</mn></mrow></msup><mo> $-(2\mathrm{x}{\phantom{A}}^2+5)=-2\mathrm{x}{\phantom{A}}^2-5$</mo><mn> $-(2\mathrm{x}{\phantom{A}}^2+5)=-2\mathrm{x}{\phantom{A}}^2-5$</mn><mo stretchy="false"> $-(2\mathrm{x}{\phantom{A}}^2+5)=-2\mathrm{x}{\phantom{A}}^2-5$</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo> $-(2\mathrm{x}{\phantom{A}}^2+5)=-2\mathrm{x}{\phantom{A}}^2-5$</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo> $-(2\mathrm{x}{\phantom{A}}^2+5)=-2\mathrm{x}{\phantom{A}}^2-5$</mo></mrow><mn> $-(2\mathrm{x}{\phantom{A}}^2+5)=-2\mathrm{x}{\phantom{A}}^2-5$</mn><msup><mtext> $-(2\mathrm{x}{\phantom{A}}^2+5)=-2\mathrm{x}{\phantom{A}}^2-5$</mtext><mrow class="MJX-TeXAtom-ORD"><mn> $-(2\mathrm{x}{\phantom{A}}^2+5)=-2\mathrm{x}{\phantom{A}}^2-5$</mn></mrow></msup><mrow class="MJX-TeXAtom-ORD"><mo> $-(2\mathrm{x}{\phantom{A}}^2+5)=-2\mathrm{x}{\phantom{A}}^2-5$</mo></mrow><mn> $-(2\mathrm{x}{\phantom{A}}^2+5)=-2\mathrm{x}{\phantom{A}}^2-5$</mn></mrow></mstyle></mrow><annotation encoding="application/x-tex"> </annotation></semantics></math>$-(2\mathrm{x}{\phantom{A}}^2+5)=-2\mathrm{x}{\phantom{A}}^2-5$</img>
$\frac{1}{x+2}$	$-\frac{1}{x+2}$
$\sqrt{2}\sin \theta -\sqrt{3}\cos 2\theta$	$-(\sqrt{2}\sin \theta -\sqrt{3}\cos 2\theta )=-\sqrt{2}\sin \theta +\sqrt{3}\cos 2\theta$

Dangantaka da Ragi

Ƙarin inverse yana da alaƙa kusa da ragi, wanda za'a iya kallonsa azaman ƙari ta amfani da juzu'i:

a − b  =  a + (−b).

Akasin haka, ana iya tunanin ƙari inverse a matsayin ragi daga sifili:

−a = 0 − a.

Wannan haɗin yana haifar da amfani da alamar ragi don duka girman girman da ragi har zuwa karni na 17. Duk da yake wannan ma'auni daidai ne a yau, an gamu da adawa a lokacin, kamar yadda wasu masana lissafin ke ganin zai iya zama ba a sani ba kuma yana haifar da kurakurai.

Ma'anar Ainihin

An ba da tsarin algebra da aka ayyana ƙarƙashin ƙari $(S,+)$ tare da ƙari ainihi $e\in S$, wani kashi $x\in S$ yana da ƙari inverse $y$ idan kuma kawai idan $y\in S$, $x+y=e$, kuma $y+x=e$ .

Ƙari yawanci ana amfani da shi ne kawai don komawa zuwa aiki na sadarwa, amma ba lallai ba ne haɗin gwiwa . Lokacin da ake tarayya, haka $(a+b)+c=a+(b+c)$, inverses na hagu da dama, idan sun kasance, za su yarda, kuma ƙari zai zama na musamman. A cikin shari'o'in da ba na tarayya ba, maƙasudin hagu da dama na iya samun sabani, kuma a cikin waɗannan lokuta, ba a la'akari da cewa akwai wani abu ba.

Ma'anar yana buƙatar ƙulli, cewa abin da ake ƙarawa $y$ a same shi a ciki $S$ . Wannan shine dalilin da ya sa duk da ƙarin da aka ayyana akan lambobi na halitta, ba ƙari ba ne ga membobinsa. Inverses masu alaƙa zasu zama lambobi mara kyau, wanda shine dalilin da yasa adadin ke da juzu'in ƙari.

Karin Misalai

• A cikin sarari vector, ƙari inverse −v (sau da yawa ana kiransa kishiyar vector na v ) yana da girma iri ɗaya da v amma akasin shugabanci.
• A cikin ilmin lissafi na zamani, madaidaicin ƙari inverse x shine lamba a haka a x ≡ 0 (mod n ) kuma koyaushe yana wanzuwa. Misali, sabanin 3 modulo 11 shine 8, kamar yadda 3 + 8 ≡ 0 (mod 11) .
• A cikin zoben Boolean, wanda ke da abubuwa $\{0,1\}$ Bugu da kari ana yawan bayyana shi azaman bambancin simmetric . Don haka $0+0=0$, $0+1=1$, $1+0=1$, kuma $1+1=0$ . Abubuwan da muke ƙarawa shine 0, kuma duka abubuwa biyu nasu ƙari ne sabanin haka $0+0=0$ kuma $1+1=0$ .

Duba kuma

• Cikakkar ƙima (mai alaƙa ta hanyar ainihi |−x | = | x | ).
• Monoid
• Inverse aiki
• Juyin Halitta (ilimin lissafi)
• Juyawa juzu'i
• Tunani (ilimin lissafi)
• Tunani mai ma'ana
• Ƙungiyar Ƙungiya