Tabel de simboluri matematice.doc

7/28/2019 Tabel de simboluri matematice.doc

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Tabel de simboluri matematiceDe la Wikipedia, enciclopedia liberSalt la:Navigare,cutare

Urmtorultabel descrie multe simboluri speciale folosite des n matematic. Pentru codurile HTML ale

simbolurilor matematice, vezi coduri HTML matematice.

Cuprins

1 Simboluri matematice de baz 2 Vezi i

3 Legturi externe

4 Caractere speciale

Simboluri matematice de baz

Simbol

Seminificaie

Explicaie ExempleSe citete

Categorie

=egalitate x =y nseamnxiy reprezint

acelai lucru sau au aceeai

valoare.

1 + 1 = 2este egal cu

oriunde

neegalitatex y nseamn cxiy nureprezint acelai lucru sau nuau aceeai valoare.

1 2nu este egal cu

diferit deoriunde

strict inegalitate x y nseamn cx este maimare decty.

xy nseamn cx mult maimic decty.

xy nseamn cx mult maimare decty.

3 < 45 > 40,003 1000000

este mai micdect,

este mai maredect,

este mult mai micdect,

este mult maimare dect

teoria ordonrii

inegalitatex y nseamn cx este mai mic

sau egal cuy.

x y nseamn cx este maimare sau egal cuy.

3 4 i 5 55 4 and 5 5

este mai mic sauegal cu,

este mai mare sauegal cu

teoria ordonrii proporionalitate yx nseamn cy = kx pentru dacy = 2x, atunciyx
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2/11

o constant k.este proporional

cuoriunde

+

adunare4 + 6 nseamn suma lui 4 i 6 2 + 7 = 9plus

aritmeticreuniune disjunct

A1 +A2 nseamn reuniuneadisjunct a mulimilorA1iA2.

A1={1,2,3,4} A2={2,4,5,7} A1 +A2 = {(1,1), (2,1),(3,1), (4,1), (2,2), (4,2),(5,2), (7,2)}

reuniuneadisjunct ntre

teoria mulimilor

diferen9 4 nseamn diferena dintre 9i 4

8 3 = 5minusaritmetic

opusul

3 nseamn opusul lui 3. (5) = 5negativ ; minusaritmeticcomplementulunei mulimi A B nseamn mulimea care

conine toate elementele dinAcare nu sunt nB.

{1,2,4} {1,3,4} = {2}minus; fr

teoria mulimilor

produs3 4 nseamn produsul lui 3 i4.

7 8 = 56ori,

nmulit cu

aritmeticprodus cartezian

XYnseamn mulimea tuturorperechilor ordonate cu primulelement din X i al doileaelement din Y.

{1,2} {3,4} = {(1,3),(1,4),(2,3),(2,4)}

produsul cartezianntre; produsul

directteoria mulimilor

produs vectorialu v nseamn produsul

vectorial al vectorilorui v

(1,2,5) (3,4,1) =

(22, 16, 2)

produs vectorial

cualgebr vectorial

/

mprire6 3 sau 6/3 nseamnmprirea lui 6 la 3

2 4 = 0,5

12 / 4 = 3mprit la

aritmetic

rdcin ptrat

x nseamn numrul pozitiv alcrui ptrat estex.

4 = 2rdcina ptrat alui; radicalul de

ordin doi dinnumere reale

rdcina ptratcomplex dacz= rexp(i) este

reprezentat n coordonate polare,atunci z= rexp(i/2).

(-1) = irdcina ptratcomplex a lui
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numere complexe

| |

valoare absolut|x| nseamn distana pe axa real(sau n planul complex) dintrexi zero.

|3| = 3, |-5| = |5||i| = 1, |3+4i| = 5

valoarea absoluta lui; modul din

numere

!factorial

n! este produsul 12...n. 4! = 1 2 3 4 = 24factorial

combinatoric

~

distribuie deprobabilitate X ~ D, nseamn c variabila

aleatoareXare distribuia deprobabilitateD.

X ~ N(0,1), distribuianormal standardare distribuia

statistic

implicaie AB nseamn c dacA esteadevrat, atunci iB esteadevrat; n caz cA este fals,

nu se poate spune nimic despreB.

poate nsemna acelai lucruca i sau poate avea sensulpentru funcii descris mai jos.

poate nsemna acelai lucru cai sau poate avea sensul de

supramulime descris mai jos.

x = 2 x2 = 4 esteadevrat, darx2 = 4 x= 2 este n general fals(deoarecex poate fi 2,dac domeniul studiatpermite).

implic; dac ..atunci

logicpropoziional

echivalen

AB nseamn cAiB auaceleai valori de adevr.

x + 5 =y +2 x + 3 =y

dac i numaidac (dnd);

echivalent culogic

propoziional

negaie logic Propoziia A este adevratdac i numai dacA este fals.

O bar oblic ce taie un operatorreprezint acelai lucru ca i ""scris n fa.

(A)Ax y (x =y)

non

logicpropoziional

conjuncie logicsau infimum ntr-o latice PropoziiaAB este adevrat

dacAiB sunt ambeleadevrate; altfel este fals.

n < 4 n >2 n = 3dac n este numr natural.

ilogic

propoziional,teoria laticelor

disjuncie logicsau supremumntr-o latice

PropoziiaAB este adevratdacA sauB (sau ambele) suntadevrate; altfel este fals.

n 4 n 2 n 3dac n este numr natural.

sau
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le=Calcul_propozi%C8%9Bional&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Echivalen%C8%9B%C4%83&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Calcul_propozi%C8%9Bional&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Calcul_propozi%C8%9Bional&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Nega%C8%9Bie_logic%C4%83&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Calcul_propozi%C8%9Bional&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Calcul_propozi%C8%9Bional&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Conjunc%C8%9Bie_logic%C4%83&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Latice&action=edit&redlink=1http://ro.wikipedia.org/wiki/Num%C4%83r_naturalhttp://ro.wikipedia.org/w/index.php?title=Calcul_propozi%C8%9Bional&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Calcul_propozi%C8%9Bional&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Latice&action=edit&redlink=1http://ro.wikipedia.org/wiki/Disjunc%C8%9Bie_logic%C4%83http://ro.wikipedia.org/w/index.php?title=Latice&action=edit&redlink=1http://ro.wikipedia.org/wiki/Num%C4%83r_natural


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logicpropoziional,

teoria laticelor

sau exclusivAfirmaiaAB este adevratdac fie A, fie B, dar nu ambele,este adevrat.AB nseamnacelai lucru.

(A)A este mereuadevrat,AA estemereu fals.

xorlogic

propoziional,

algebr boolean

cuantificatoruniversal

x:P(x) nseamnP(x) esteadevrat pentru toix dindomeniu.

nN: n2 n.oricare; pentru

fiecarelogica

predicatelor

cuantificatorexistenial x:P(x) nseamn c exist cel

puin unx astfel nctP(x) esteadevrat.

nN: n este par.existlogica

predicatelor

!

cuantificator deunicitate

!x:P(x) nseamn c existexact unx astfel nctP(x) esteadevrat.

! nN: n + 5 = 2n.exist un(o)

unic()exist i e unic()

logicapredicatelor

:=

:

definiie x :=y saux y nseamn cxeste definit ca un alt nume pentru

y (de observat c poate avea ialte sensuri, precumcongruen).

P:Q nseamn cPeste

definit astfel nct, din punct devedere logic, este echivalent cuQ.

coshx := (1/2)(expx +exp (x))

A XORB :(AB) (AB)

se definete ca

oriunde

{ , }

acolade demulime {a,b,c}nseamn mulimea

format din a, bi c.N = {0,1,2,...}

mulimeateoria mulimilor

{ : }

{ | }

notaie deconstrucie a unei

mulimi {x :P(x)} sau {x |P(x)}nseamn mulimea acelorxpentru careP(x) este adevrat.

{nN : n2 < 20} ={0,1,2,3,4}

mulimeaelementelor cuproprietatea cteoria mulimilor

mulimea vid
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it&redlink=1http://ro.wikipedia.org/wiki/Algebr%C4%83_boolean%C4%83http://ro.wikipedia.org/w/index.php?title=Cuantificator_universal&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Cuantificator_universal&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Logica_predicatelor&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Logica_predicatelor&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Cuantificator_existen%C8%9Bial&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Cuantificator_existen%C8%9Bial&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Logica_predicatelor&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Logica_predicatelor&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Cuantificator_de_unicitate&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Cuantificator_de_unicitate&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Logica_predicatelor&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Logica_predicatelor&action=edit&redlink=1http://ro.wikipedia.org/wiki/Defini%C8%9Biehttp://ro.wikipedia.org/w/index.php?title=Congruen%C8%9B%C4%83&action=edit&redlink=1http://ro.wikipedia.org/wiki/Mul%C8%9Bimehttp://ro.wikipedia.org/w/index.php?title=Teoria_naiv%C4%83_a_mul%C8%9Bimilor&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Nota%C8%9Bie_de_construc%C8%9Bie_a_unei_mul%C8%9Bimi&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Nota%C8%9Bie_de_construc%C8%9Bie_a_unei_mul%C8%9Bimi&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Nota%C8%9Bie_de_construc%C8%9Bie_a_unei_mul%C8%9Bimi&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Teoria_naiv%C4%83_a_mul%C8%9Bimilor&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Mul%C8%9Bimea_vid%C4%83&action=edit&redlink=1


5/11

{}

nseamn mulimea cu nici unelement. {} este o notaieechivalent.

{nN : 1 < n2 < 4} =mulimea vid

teoria mulimilor

apartenen

aSnseamn c a este unelement al mulimii S; a S

nseamn c a nu este un elemental mulimii S.

(1/2)1N

21 N

aparine lui, esteinclus n;

nu aparine lui, nu

este inclus noriunde, teoria

mulimilor

submulime (submulime)AB nseamnc fiecare element dinA este ielement al luiB.

(submulime proprie)ABnseamn cAB darA B.

A BA; QR

este inclus n;este o submulime

pentru; estesubmulime a luiteoria mulimilor

superset AB nseamn c fiecareelement dinB este i element alluiA.

AB nseamn cAB darA B.AB este echivalent cuBA,AB este echivalent cuBA.

ABB; RQ

include; este osupramulimepentru; este

supramulime alui

teoria mulimilor

reuniune Reuniune exclusiv (vezi idiferen simetric):ABnseamn mulimea care coninetoate elementele luiA, i toateelementele luiB, dar nu ielementele lor comune."A sauB, dar nu amndou".

Reuniune inclusiv:ABnseamn mulimea care coninetoate elementele luiA, i toateelementele luiB."A sauB sau amndou".

ABAB =B

AB = {x |xAxB)}

reuniunea ntre

teoria mulimilor

intersecie demulimi A B nseamn mulimea ce

conine elementele comune dinAiB

{xR:x2 = 1} = {1}intersecia dintreteoria mul imilor

\

set-theoretic

complementA \B nseamn mul imea cecon ine elementele pe care A leare n plus fa de B

{1,2,3,4} \ {3,4,5,6} ={1,2}diferen ateoria mul imilor

( )valoarea func iei

f(x) nseamn 'f de x', sauvaloarea luifn elementulx.

Dacf(x) :=x2, atuncif(3) =32 = 9.

deteoria mul imilor
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6/11

modificatori depreceden Se efectueaz nti opera iile din

paranteze.(8/4)/2 = 2/2 = 1, dar 8/(4/2) = 8/2 = 4.paranteze

oriunde

f:XYfunctie sgeat f:X Ynseamn c func ia f

transport elementele luiXncele din Y.

Letf: Z N be defined byf(x) :=x2.

de ... lateoria mul imilor

o

func iacompunere foge functia, fiind (fog)(x) =

f(g(x)).iff(x) := 2x, i g(x) :=x + 3,apoi (fog)(x) = 2(x + 3).compus cu

teoria mul imilor

N

numere naturaleN nseamn {0,1,2,3,...}, dar a sevedea i numere naturale pentruo alt conven ie.

{|a| : a Z} = NN

numr

Z

numere ntregi Z nseamn {...,3,2,1,0,1,2,3,...}.

{a : |a| N} = ZZ

numr

Q

numere ra ionaleQ nseamn {p/q :p,qZ,q 0}.

3.14 Q

Q

Q

numr

R

numere reale

Rnseamn setul de numerereale.

R

(1) RR

numr

C

numere complexe

C nseamn {a + bi : a,bR}. i = (1) CC

numr

infinitate este un element al mul imiireale extinse i este mai mare ca

orice alt numr real, fiin deseorintalnit n limite matematice.

limx0 1/|x| = infinitate

numr

pi este raportul dintre lungimeacercului i diametrul su.Valorea lui este 3.1415....

A = r este aria unui cerccu raza r

pigeometrieeuclidian

|| ||

norma||x|| este norma unui elementxdin spa iul vectorial normat .

||x+y|| ||x|| + ||y||norma lui;

lungimea lui

algebr liniar

nsumarek=1nak nseamn a1 + a2 + ... +an.

k=14k2 = 12 + 22 + 32 + 42 =1 + 4 + 9 + 16 = 30

sum peste ...de ... la ... din

oriunde
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7/11

nmul ire

k=1nak nseamn a1a2an.k=14 (k+ 2) = (1 + 2)(2 +2)(3 + 2)(4 + 2) = 3 4 5 6 = 360

produs peste ... de... la ... din

oriundeProdus cartezian

i=0nYi nseamn setul tuturor

(n+1)-uplurilor(y0,...,yn).

n=13R= Rnprodusul cartezian

dintre; produsul

direct dintrealgebr

'

Derivatf'(x) este derivata func iei fnpunctulx,ex: tangenta la graficulluifnx.

Dacf(x) :=x2,atuncif'(x) = 2x

prim; derivatalui

analizmatematic

Integralanedefinit sauantiderivat f(x) dx nseamn o func ie a

crui derivat ef.x2 dx =x3/3 + C

integralnedefinit din ;

calculusIntegrala definit

abf(x) dx nseamn aria cu semndintre axax i grficul func iei lui

fntrex = a i x = b.0b x2 dx = b3/3;

integrala de la ...pn la ....

analiz

matematic

gradientf(x1, , xn) este vectorulderivatelor par iale ( df/ dx1, ,df/ dxn).

Dacf(x,y,z) := 3xy +z,atunci f= (3y, 3x, 2z)

Nabla, gradientdin

analizmatematic

derivat par ial Cuf(x1, , xn), f/xi estederivata luifn func ie de x i,celelalte variabile pstrndu-seconstante.

dacf(x,y) := x2y, atuncif/x = 2xy

derivat par ial din

calculusfrontiera

Mnseamn frontiera mul imiiM

{x : ||x|| 2} = {x : ||x|| =2}

frontieratopologie

perpendicular xy nseamnx esteperpendicular pey; sau maigeneralx e ortogonal pey.

Dac lm i mn atunci l|| n.

e perpendicular pegeometrie

element minim

(cel mai mic) x = nseamn c x este cel maimic element.

x :x = Elementul minimt

lattice theory

entailment AB means the sentenceA

entails the sentenceB, that isAA A

entails
http://ro.wikipedia.org/w/index.php?title=Multiplicare&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Multiplicare&action=edit&redlink=1http://ro.wikipedia.org/wiki/Produs_cartezianhttp://ro.wikipedia.org/w/index.php?title=N-uplu&action=edit&redlink=1http://ro.wikipedia.org/wiki/Algebr%C4%83http://ro.wikipedia.org/wiki/Derivat%C4%83http://ro.wikipedia.org/wiki/Analiz%C4%83_matematic%C4%83http://ro.wikipedia.org/wiki/Analiz%C4%83_matematic%C4%83http://ro.wikipedia.org/wiki/Integrala_nedefinit%C4%83http://ro.wikipedia.org/wiki/Integrala_nedefinit%C4%83http://ro.wikipedia.org/w/index.php?title=Calculus&action=edit&redlink=1http://ro.wikipedia.org/wiki/Integrala_definit%C4%83http://ro.wikipedia.org/wiki/Analiz%C4%83_matematic%C4%83http://ro.wikipedia.org/wiki/Analiz%C4%83_matematic%C4%83http://ro.wikipedia.org/wiki/Gradienthttp://ro.wikipedia.org/w/index.php?title=Operatorul_Nabla&action=edit&redlink=1http://ro.wikipedia.org/wiki/Gradienthttp://ro.wikipedia.org/wiki/Analiz%C4%83_matematic%C4%83http://ro.wikipedia.org/wiki/Analiz%C4%83_matematic%C4%83http://ro.wikipedia.org/wiki/Derivat%C4%83_par%C8%9Bial%C4%83http://ro.wikipedia.org/wiki/Derivat%C4%83_par%C8%9Bial%C4%83http://ro.wikipedia.org/w/index.php?title=Calculus&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Frontier%C4%83_(topologie)&action=edit&redlink=1http://ro.wikipedia.org/wiki/Topologiehttp://ro.wikipedia.org/w/index.php?title=Perpendicular&action=edit&redlink=1http://ro.wikipedia.org/wiki/Geometriehttp://ro.wikipedia.org/w/index.php?title=Element_minim_(cel_mai_mic)&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Element_minim_(cel_mai_mic)&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Lattice_(order)&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Entailment&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Multiplicare&action=edit&redlink=1http://ro.wikipedia.org/wiki/Produs_cartezianhttp://ro.wikipedia.org/w/index.php?title=N-uplu&action=edit&redlink=1http://ro.wikipedia.org/wiki/Algebr%C4%83http://ro.wikipedia.org/wiki/Derivat%C4%83http://ro.wikipedia.org/wiki/Analiz%C4%83_matematic%C4%83http://ro.wikipedia.org/wiki/Analiz%C4%83_matematic%C4%83http://ro.wikipedia.org/wiki/Integrala_nedefinit%C4%83http://ro.wikipedia.org/wiki/Integrala_nedefinit%C4%83http://ro.wikipedia.org/w/index.php?title=Calculus&action=edit&redlink=1http://ro.wikipedia.org/wiki/Integrala_definit%C4%83http://ro.wikipedia.org/wiki/Analiz%C4%83_matematic%C4%83http://ro.wikipedia.org/wiki/Analiz%C4%83_matematic%C4%83http://ro.wikipedia.org/wiki/Gradienthttp://ro.wikipedia.org/w/index.php?title=Operatorul_Nabla&action=edit&redlink=1http://ro.wikipedia.org/wiki/Gradienthttp://ro.wikipedia.org/wiki/Analiz%C4%83_matematic%C4%83http://ro.wikipedia.org/wiki/Analiz%C4%83_matematic%C4%83http://ro.wikipedia.org/wiki/Derivat%C4%83_par%C8%9Bial%C4%83http://ro.wikipedia.org/w/index.php?title=Calculus&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Frontier%C4%83_(topologie)&action=edit&redlink=1http://ro.wikipedia.org/wiki/Topologiehttp://ro.wikipedia.org/w/index.php?title=Perpendicular&action=edit&redlink=1http://ro.wikipedia.org/wiki/Geometriehttp://ro.wikipedia.org/w/index.php?title=Element_minim_(cel_mai_mic)&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Element_minim_(cel_mai_mic)&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Lattice_(order)&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Entailment&action=edit&redlink=1


8/11

every model in whichA is true,model theory

inference

xy meansy is derived fromx. A B B A

infers or isderived from

propositionallogic,predicate

logic

normal subgroupNG means thatNis a normalsubgroup of group G.

Z(G) Gis a normalsubgroup of

group theory

/quotient group

G/Hmeans the quotient of groupGmodulo its subgroupH.

{0, a, 2a, b, b+a, b+2a} /{0, b} = {{0, b}, {a, b+a},{2a, b+2a}}

modteoria grupurilor

izomorfism G Hnseamn c grupul G eizomorf cu grupulH

Q / {1, 1} V,unde Q este quaterniongroup i Veste grupul Kleinde 4 elemente.

e izomorf cu

teoria grupurilor

egal aproximativx y nseamnx esteaproximativ egal cuy

3.14159este aproximativ

egal cuoriunde

,

( | )

< , >

:

produs scalarx,y nseamn produsul scalaral luix i y.n cadrul spa iilor euclidiene seobi nue te de a nota produsul scalar att prin (x,y) ct i prin

xy.Pentru matrice se poate utilizasemnul :.

n spa iul euclidian 2

produsul scalaral vectorilorx = (2, 3) i y = (1, 5) este:x, y = 2 1 + 3 5 =13

produs scalar

algebra liniar

Produs tensorialV Unseamn produsultensorial dintre V i U.

{1, 2, 3, 4} {1,1,2} =

{{1, 2, 3, 4}, {1, 2, 3, 4},{2, 4, 6, 8}}produs tensorialalgebr liniar

Constant fizic

ntiin, o constant fizic este o mrime fizic a crei valoare numeric este fix.

Sunt multe constante folosite n tiine, unele dintre cele mai celebre fiind: constanta lui Planckinumrul lui Avogadro. Constantele pot fi de multe feluri; unele, ca lungimea Planckreprezint o distanfizic fundamental, altele ca viteza luminii semnific viteza maxim n univers.

Mai jos este o lista cu constante fizice:
http://ro.wikipedia.org/w/index.php?title=Model_theory&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Inference&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Propositional_calculus&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Propositional_calculus&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Predicate_logic&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Predicate_logic&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Normal_subgroup&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Group_theory&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Quotient_group&action=edit&redlink=1http://ro.wikipedia.org/wiki/Modulohttp://ro.wikipedia.org/w/index.php?title=Teoria_grupurilor&action=edit&redlink=1http://ro.wikipedia.org/wiki/Izomorfismhttp://ro.wikipedia.org/w/index.php?title=Quaternion_group&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Quaternion_group&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Teoria_grupurilor&action=edit&redlink=1http://ro.wikipedia.org/wiki/Produs_scalarhttp://ro.wikipedia.org/wiki/Produs_scalarhttp://ro.wikipedia.org/wiki/Algebra_liniar%C4%83http://ro.wikipedia.org/w/index.php?title=Produs_tensorial&action=edit&redlink=1http://ro.wikipedia.org/wiki/Algebr%C4%83_liniar%C4%83http://ro.wikipedia.org/wiki/%C8%98tiin%C8%9B%C4%83http://ro.wikipedia.org/wiki/%C8%98tiin%C8%9B%C4%83http://ro.wikipedia.org/wiki/%C8%98tiin%C8%9B%C4%83http://ro.wikipedia.org/wiki/%C8%98tiin%C8%9B%C4%83http://ro.wikipedia.org/wiki/%C8%98tiin%C8%9B%C4%83http://ro.wikipedia.org/wiki/%C8%98tiin%C8%9B%C4%83http://ro.wikipedia.org/wiki/M%C4%83rime_fizic%C4%83http://ro.wikipedia.org/wiki/Constanta_lui_Planckhttp://ro.wikipedia.org/wiki/Num%C4%83rul_lui_Avogadrohttp://ro.wikipedia.org/wiki/Num%C4%83rul_lui_Avogadrohttp://ro.wikipedia.org/w/index.php?title=Lungimea_Planck&action=edit&redlink=1http://ro.wikipedia.org/wiki/Viteza_luminiihttp://ro.wikipedia.org/wiki/Univershttp://ro.wikipedia.org/w/index.php?title=Model_theory&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Inference&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Propositional_calculus&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Propositional_calculus&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Predicate_logic&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Predicate_logic&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Normal_subgroup&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Group_theory&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Quotient_group&action=edit&redlink=1http://ro.wikipedia.org/wiki/Modulohttp://ro.wikipedia.org/w/index.php?title=Teoria_grupurilor&action=edit&redlink=1http://ro.wikipedia.org/wiki/Izomorfismhttp://ro.wikipedia.org/w/index.php?title=Quaternion_group&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Quaternion_group&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Teoria_grupurilor&action=edit&redlink=1http://ro.wikipedia.org/wiki/Produs_scalarhttp://ro.wikipedia.org/wiki/Produs_scalarhttp://ro.wikipedia.org/wiki/Algebra_liniar%C4%83http://ro.wikipedia.org/w/index.php?title=Produs_tensorial&action=edit&redlink=1http://ro.wikipedia.org/wiki/Algebr%C4%83_liniar%C4%83http://ro.wikipedia.org/wiki/%C8%98tiin%C8%9B%C4%83http://ro.wikipedia.org/wiki/M%C4%83rime_fizic%C4%83http://ro.wikipedia.org/wiki/Constanta_lui_Planckhttp://ro.wikipedia.org/wiki/Num%C4%83rul_lui_Avogadrohttp://ro.wikipedia.org/w/index.php?title=Lungimea_Planck&action=edit&redlink=1http://ro.wikipedia.org/wiki/Viteza_luminiihttp://ro.wikipedia.org/wiki/Univers


9/11

Constant SimbolU.M

.

Valoare cf.

CODATA 2006[1]Valoare cf.

STAS 2848-89[2]
http://ro.wikipedia.org/wiki/Constante_fizice#cite_note-1http://ro.wikipedia.org/wiki/Constante_fizice#cite_note-2http://ro.wikipedia.org/wiki/Constante_fizice#cite_note-1http://ro.wikipedia.org/wiki/Constante_fizice#cite_note-2


10/11

viteza luminii n vid ms-1 299 792 458 (prin def.) 299 792 458 (prin def.)

permeabilitatea viduluiN A-2

410-7 (prin def.)= 12,566 370 614...10-7

410-7 (prin def.)= 12,566 370 614...10-7

permitivitatea viduluiFm-1 8,854 187 81710

-12 8,854 187 81710-12

impedanacaracteristic a vidului

376,730 313 461... (prindef.)

constanta gravitaionalm3kg-1s-2

6,674 28(67)10-11 6,672 59(85)10-11

constanta lui Planck Js 6,626 068 76(52)10-34 6,626 075 5(40)10-34

constanta lui Dirac Js 1,054 571 596(82)10-34

masa lui Planck kg 2,176 44(11)10-8 2,176 71(14)10-8

lungimea lui Planck m 1,616 252(81)10-35 1,616 05(10)10-35

timpul lui Planck s 5,391 24(27)10-44 5,390 56(34)10-44

sarcina elementar C 1,602 176 487(40)10-19 1,602 177 33(49)10-19

masa de repaus aelectronului

kg 9,109 382 15(45)10-31 9,109 388 7(54)10-31

masa de repaus aprotonului

kg 1,672 621 637(83)10-27 1,672 623 1(10)10-27

masa de repaus aneutronului

kg 1,674 927 211(84)10-27 1,674 928 6(10)10-27

unitatea atomic demas

kg 1,660 538 782(83)10-27 1,660 540 2(10)10-27

numarul lui Avogadro - 6,022 141 79(30)1023 6,022 136 7(36)1023

constanta lui Boltzmann JK-1 1,380 6504(24)10-23 1,380 658(12)10-23

constanta lui FaradayCmol-1

9,648 533 99(24)104 9,648 540 2(10)104

constanta universal a

gazului ideal

JK-1

mol-1 8,314 472(15) 8,314 510(70)

zero pe scala Celsius C -273,15 (prin def.) -273,15 (prin def.)

volumul molar algazului ideal,lap = 1 atm, t= 0C

m310-3mo

22,413 996(39) 22,414 10(19)
http://ro.wikipedia.org/wiki/Viteza_luminiihttp://ro.wikipedia.org/w/index.php?title=Permeabilitatea&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Permitivitatea&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Impedan%C8%9Ba&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Impedan%C8%9Ba&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Impedan%C8%9Ba&action=edit&redlink=1http://ro.wikipedia.org/wiki/Constanta_gravita%C8%9Bional%C4%83http://ro.wikipedia.org/wiki/Constanta_gravita%C8%9Bional%C4%83http://ro.wikipedia.org/wiki/Constanta_gravita%C8%9Bional%C4%83http://ro.wikipedia.org/wiki/Constanta_lui_Planckhttp://ro.wikipedia.org/wiki/Constanta_lui_Planckhttp://ro.wikipedia.org/w/index.php?title=Masa_lui_Planck&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Lungimea_lui_Planck&action=edit&redlink=1http://ro.wikipedia.org/wiki/Timpul_lui_Planckhttp://ro.wikipedia.org/wiki/Sarcina_elementar%C4%83http://ro.wikipedia.org/w/index.php?title=Masa_de_repaus&action=edit&redlink=1http://ro.wikipedia.org/wiki/Electronhttp://ro.wikipedia.org/w/index.php?title=Masa_de_repaus&action=edit&redlink=1http://ro.wikipedia.org/wiki/Protonhttp://ro.wikipedia.org/w/index.php?title=Masa_de_repaus&action=edit&redlink=1http://ro.wikipedia.org/wiki/Neutronhttp://ro.wikipedia.org/wiki/Unitatea_atomic%C4%83_de_mas%C4%83http://ro.wikipedia.org/wiki/Unitatea_atomic%C4%83_de_mas%C4%83http://ro.wikipedia.org/wiki/Numarul_lui_Avogadrohttp://ro.wikipedia.org/wiki/Constanta_lui_Boltzmannhttp://ro.wikipedia.org/w/index.php?title=Constanta_lui_Faraday&action=edit&redlink=1http://ro.wikipedia.org/wiki/Constanta_universal%C4%83_a_gazului_idealhttp://ro.wikipedia.org/wiki/Constanta_universal%C4%83_a_gazului_idealhttp://ro.wikipedia.org/wiki/Celsiushttp://ro.wikipedia.org/wiki/Celsiushttp://ro.wikipedia.org/wiki/Viteza_luminiihttp://ro.wikipedia.org/w/index.php?title=Permeabilitatea&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Permitivitatea&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Impedan%C8%9Ba&action=edit&redlink=1http://ro.wikipedia.org/wiki/Constanta_gravita%C8%9Bional%C4%83http://ro.wikipedia.org/wiki/Constanta_lui_Planckhttp://ro.wikipedia.org/wiki/Constanta_lui_Planckhttp://ro.wikipedia.org/w/index.php?title=Masa_lui_Planck&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Lungimea_lui_Planck&action=edit&redlink=1http://ro.wikipedia.org/wiki/Timpul_lui_Planckhttp://ro.wikipedia.org/wiki/Sarcina_elementar%C4%83http://ro.wikipedia.org/w/index.php?title=Masa_de_repaus&action=edit&redlink=1http://ro.wikipedia.org/wiki/Electronhttp://ro.wikipedia.org/w/index.php?title=Masa_de_repaus&action=edit&redlink=1http://ro.wikipedia.org/wiki/Protonhttp://ro.wikipedia.org/w/index.php?title=Masa_de_repaus&action=edit&redlink=1http://ro.wikipedia.org/wiki/Neutronhttp://ro.wikipedia.org/wiki/Unitatea_atomic%C4%83_de_mas%C4%83http://ro.wikipedia.org/wiki/Unitatea_atomic%C4%83_de_mas%C4%83http://ro.wikipedia.org/wiki/Numarul_lui_Avogadrohttp://ro.wikipedia.org/wiki/Constanta_lui_Boltzmannhttp://ro.wikipedia.org/w/index.php?title=Constanta_lui_Faraday&action=edit&redlink=1http://ro.wikipedia.org/wiki/Constanta_universal%C4%83_a_gazului_idealhttp://ro.wikipedia.org/wiki/Constanta_universal%C4%83_a_gazului_idealhttp://ro.wikipedia.org/wiki/Celsiushttp://ro.wikipedia.org/wiki/Celsius


11/11

l-1

atmosfera standard atm Pa 101 325 (prin def.) 101 325 (prin def.)

constanta structurii fine-

7,297 352 5376(50)10-3

137,035 999 679(94)7,297 353 08(33)10-3

137,035 989 5(61)

raza lui Bohr m 5,291 772 085 9(36)10-11 5,291 772 49(24)10-11

energia Hartree J 4,359 743 94(22)10-18 4,359 748 2(26)10-18

constanta lui Rydberg m-1 1,097 373 156 8527(83)107 1,097 373 153 4(13)107

magnetonul luiProcopiu-Bohr

JT-1 9,274 009 15(23)10-24 9,274 015 4(31)10-24

momentul magnetic alelectronului

JT-1 -9,284 763 77(23)10-24 -9,284 770 1(31)10-24

factorul Land alelectronuluisin.: factorulgalelectronului

-

-2,002 319 304 3622(15)

-2,002 319 304 386(20)

magnetonul nuclear JT-1 5,050 783 24(13)10-27 5,050 786 6(17)10-27

momentul magnetic alprotonului

JT-1 1,410 606 662(37)10-26 1,410 607 61(47)10-26

momentul magneticecranat al protonuluintr-o sfer de H2O,25C

JT-1

1,410 570 419(38)10-26

1,410 571 38(47)10-26

raportul giromagnetic alprotonului

s-1T-1

2,675 222 099(70)108 2,675 221 28(81)108

raportul giromagneticnecorectat al protonuluintr-o sfer de H2O,

25C

MHzT-1

42,577 4821(11) 42,577 469(15)

constanta Stefan-Boltzmann

Wm-2K-4

5,670 400(40)10-8 5,670 51(19)10-8

prima constant aradiaiei

Wm2

3,741 771 18(19)10-16 3,741 774 9(22)10-16

a doua constant aradiaiei

mK 1,438 7752(25)10-2 1,438 769(12)10-2

Unele "constante" sunt n realitate artificii ale sistemului de uniti utilizat, de exemplu mkssau cgs. nuniti naturale, unele din aceste aa zise constante fizice se dovedesc a fi doar simpli factori deconversie.
http://ro.wikipedia.org/wiki/Constanta_structurii_finehttp://ro.wikipedia.org/w/index.php?title=Raza_lui_Bohr&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Energia_Hartree&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Constanta_lui_Rydberg&action=edit&redlink=1http://ro.wikipedia.org/wiki/Magnetonul_lui_Procopiu-Bohrhttp://ro.wikipedia.org/wiki/Magnetonul_lui_Procopiu-Bohrhttp://ro.wikipedia.org/w/index.php?title=Momentul_magnetic_al_electronului&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Momentul_magnetic_al_electronului&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Magnetonul_nuclear&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Momentul_magnetic_al_protonului&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Momentul_magnetic_al_protonului&action=edit&redlink=1http://ro.wikipedia.org/wiki/Celsiushttp://ro.wikipedia.org/wiki/Celsiushttp://ro.wikipedia.org/wiki/Celsiushttp://ro.wikipedia.org/wiki/Celsiushttp://ro.wikipedia.org/w/index.php?title=Constanta_Stefan-Boltzmann&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Constanta_Stefan-Boltzmann&action=edit&redlink=1http://ro.wikipedia.org/wiki/SIhttp://ro.wikipedia.org/wiki/SIhttp://ro.wikipedia.org/w/index.php?title=Cgs&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Cgs&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Unit%C4%83%C8%9Bi_naturale&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Unit%C4%83%C8%9Bi_naturale&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Unit%C4%83%C8%9Bi_naturale&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Unit%C4%83%C8%9Bi_naturale&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Factor_de_conversie&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Factor_de_conversie&action=edit&redlink=1http://ro.wikipedia.org/wiki/Constanta_structurii_finehttp://ro.wikipedia.org/w/index.php?title=Raza_lui_Bohr&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Energia_Hartree&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Constanta_lui_Rydberg&action=edit&redlink=1http://ro.wikipedia.org/wiki/Magnetonul_lui_Procopiu-Bohrhttp://ro.wikipedia.org/wiki/Magnetonul_lui_Procopiu-Bohrhttp://ro.wikipedia.org/w/index.php?title=Momentul_magnetic_al_electronului&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Momentul_magnetic_al_electronului&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Magnetonul_nuclear&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Momentul_magnetic_al_protonului&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Momentul_magnetic_al_protonului&action=edit&redlink=1http://ro.wikipedia.org/wiki/Celsiushttp://ro.wikipedia.org/wiki/Celsiushttp://ro.wikipedia.org/w/index.php?title=Constanta_Stefan-Boltzmann&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Constanta_Stefan-Boltzmann&action=edit&redlink=1http://ro.wikipedia.org/wiki/SIhttp://ro.wikipedia.org/w/index.php?title=Cgs&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Unit%C4%83%C8%9Bi_naturale&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Factor_de_conversie&action=edit&redlink=1http://ro.wikipedia.org/w/index.php?title=Factor_de_conversie&action=edit&redlink=1

Tabel de simboluri matematice.doc

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