IS 1890-11: Quantities and Units, Part 11: Mathematical signs and symbols for use in the physical sciences and technology

34 Pages·1995·2.1 MB·English

by  Bureau of Indian Standards

इंटरनेट मानक
Disclosure to Promote the Right To Information
Whereas the Parliament of India has set out to provide a practical regime of right to
information for citizens to secure access to information under the control of public authorities,
in order to promote transparency and accountability in the working of every public authority,
and whereas the attached publication of the Bureau of Indian Standards is of particular interest
to the public, particularly disadvantaged communities and those engaged in the pursuit of
education and knowledge, the attached public safety standard is made available to promote the
timely dissemination of this information in an accurate manner to the public.
“जान1 का अ+धकार, जी1 का अ+धकार” “प0रा1 को छोड न’ 5 तरफ”
Mazdoor Kisan Shakti Sangathan Jawaharlal Nehru
“The Right to Information, The Right to Live” “Step Out From the Old to the New”
IS 1890-11 (1995): Quantities and Units, Part 11:
Mathematical signs and symbols for use in the physical
sciences and technology [MSD 10: Social Responsibility]
“!ान $ एक न’ भारत का +नम-ण”
Satyanarayan Gangaram Pitroda
““IInnvveenntt aa NNeeww IInnddiiaa UUssiinngg KKnnoowwlleeddggee””
“!ान एक ऐसा खजाना > जो कभी च0राया नहB जा सकता हहहहै””ै”
Bhartṛhari—Nītiśatakam
“Knowledge is such a treasure which cannot be stolen”

SI 0981 (Part )11 : 5991
0SI 11-13 : 2991

Indian Standard
SEITITNAUQ AND UNITS
TRAP 11 LACITAMEHTAM SNGIS DNA SLOBMYS FOR ESU NI EHT
LACISYHP SECNEICS DNA YGOLONHCET
Second Revision )
(
UDC 180.35

0 SIB 5991
BUREAU OF INDIAN STAldARDS
KANAM ,NAVAHB 9 RUDAHAB HAHS RAFAZ GRAM
NEW IHLED 200011
August 5991 ecirP puorG 01
Basic Standards Sectional Committee, MSD 1
NATIONAL FOREWORD
This Indian Standard (Part 11) (Second Revision) which is identical with IS0 31-l 1 : 1992, issued by
the International Organization for Standardization (ISO) was adopted by the Bureau of Indian Standards
on the recommendation of the Basic Standards Sectional Committee (MSD 1) and approval of the
Management and Systems Division Council.
The text of the IS0 Standard has been approved as suitable for publication as Indian Standard without
deviations. Certain conventions are, however, not identical to those used in Indian Standards. Attention
is particularly drawn to the following:
Comma (J has been used as a decimal marker while in Indian Standards the current practice is
to use a point (.) as the decimal marker.
Wherever the words ‘International Standard’ appear, referring to this standard, they should be
read as ‘Indian Standard’.
This standard was first published in 1961 and then revised in 1982. In this second revision, following
changes have been made:
a) A new clause on co-ordinate systems has been added, as Introduction to the standard; and
b) Somenewitemshavebeenaddedinoldclausessuchas11-4.14to11-4.17,11-4.33,11-5.15,
11-5-16, 11-6.1, 11-6.3, 11-6.4, 11-12.1 toll-12.3
In the adopted standard, normative references appear to certain International Standards for which
Indian Standards also exist. The corresponding Indian Standards which are to be substituted in their
place are listed below along with their degree of equivalence for the edition indicated:
International Standard Corresponding Indian Degree of
Standard Equivalence
IEC 27-l : 1971 IS 3700 (Part 1) : 1983 Letter sym- Equivalent
bols and signs used in electric

technology : Part 1 General

guidance on symbols and sub-
scripts (first revision)
ADDITIONAL INFORMATION
IS 189O/ISO 31 consists of the following parts, under the general title ‘Quantities and Units’:
International Standard Corresponding Indian Degree of
Standard Equivalence
IS0 31-O : 1992 IS 1890 (Part 0) : 1995 Quantities Identical
and units : Part 0 General principles
(first revision)
ISO31-1 : 1992 IS 1890 (Part 1) : 1995 Quantities Identical
and units : Part 1 Space and time
(third revision)
IS0 31-2 : 1992 IS 1890 (Part 2) : 1995 Quantities Identical
and units : Part 2 Periodic and re-
lated phenomena (second revision)
(Continued on third coverj
IS 1890 (Part 11) : 1995
IS0 31-11 : 1992
Indian Standard
SEITITNAUQ AND UNITS
PART 11 MATHEidATICAL !ilG@ AND SYMBOLS FOR USE IN THE
PHYSICAL SCIENCES AND TECHNOLOGY
Second Revision )
(
1 Scope fo siht trap fo 0SI .13 tA eht time fo noitacilbup eht
noitide detacidni saw .dilav llA sdradnats era tcejbus
sihT trap fo 0SI 13 sevig lareneg noitamrofni tuoba ot ,noisiver dna ot-seitrap stnemeerga desab no siht
lacitamehtam sngis dna ,slobmys rieht ,sgninaem trap fo 0SI 13 era degaruocne ot etagitsevni eht
labrev stnelaviuqe dna .snoitacilppa ytilibissop fo gniylppa eht most tnecer noitide fo eht
dradnats detacidni .woleb Members fo CEI dna 0SI
ehT snoitadnemmocer ni siht trap fo 0SI 13 era -ni niatniam sretsiger fo yltnerruc dilav lanoitanretnI
dednet ylniam rof esu ni eht lacisyhp secneics dna .sdradnatS
.ygolonhcet
0SI ,2991:0-13 Quantities and units - Pat-t 0: Gen-
2 Normative reference eral principles.
ehT gniwollof dradnats sniatnoc snoisivorp ,hcihw
hguorht ecnerefer ni siht ,txet etutitsnoc snoisivorp
SI 0981 traP( )11 : 5991
0SI 11-13 : 2991
3 LACITAMEHTAM CIGOL
,lobmyS
metI .oN noitacilppA emaN fo lobmys ,gninaeM labrev tnelaviuqe dna skramer
ngis
1.3-11 A qAP noitcnujnoc ngis P and q
(I .2-l )I
2.3-11 v Pvq noitcnujsid ngis p ro q (or )htob
I( )2.2-l
3.3-11 7 noitagen ngis noitagen fo p; ton p; non p
(I )3.2-I
4.3-11 * P=+4 noitacilpmi ngis if p neht q; p seilpmi q ’ _
(I )4.2-l
naC osla eb nettirw q (: p.
semitemoS + is .desu
5.3-11 i PO4 ecnelaviuqe ngis p + q dna q =t. p; p si tnelaviuqe ot q
(I )5.2-I
semitemoS ++ si .desu
6.3-11 V AexV p(x) lasrevinu reifitnauq rof yreve x gnignoleb ot A, eht noitisoporp
I( )6-2-l ( Vx E A) P(X) p(x) si eurt
fI ti si raelc from eht txetnoc hcihw tes A
si gnieb ,deredisnoc eht noitaton xV p(x)
nac eb .desu

,AexroF ees .1.4-11

7.3-11 3 3xcA p(x) laitnetsixe reifitnauq ereht stsixe na x gnignoleb ot A rof hcihw
I( )7.2-l (3x~A) P(X) p(x) si eurt
fI ti si raelc from eht txetnoc hcihw tes A
si gnieb ,deredisnoc eht noitaton 3 x p(x)
nac eb .desu
For x E A, see .1.4-11
3! or i si desu ot etacidni eht ecnetsixe
fo eno dna ylno eno tnemele rof hcihw
p(x) is .eurt

2
IS 1890 (Part 11) : 1995
IS0 31-11 : 1992
4 SETS
Symbol,
Item No. Application Meaning, verbal equivalent Remarks and examples
sign
11-4.1 E XEA ‘x sgnoleb ot A; x si na
17.I-II( tnemele fo eht tes A
2.4-11 $ YEA y seod ton belong to A; ehT lobmys $ si osla .desu
(1 )2.1-l y si ton na tnemele fo eht
tes A
3.411 3 A~x eht tes A sniatnoc x (as A 3 x sah eht same gninaem sa x E A.
(I l-1.3) )tnemele
4.4-11 $ Y$A eht tes A seod ton niatnoc A $ y sah eht same gninaem sa y 4 A.
(1 )4.7-l y (as )tnemele ehT lobmys $ si osla .desu
5.4-11 ( ) ,,x( ,3 I... ]”X tes htiw stnemele oslA erehw I setoned a tes fo
(xi5 E I},
.secidni
(II-1.q Xl,$ t ...xt,
1 6.4-l 11( xI l A (PI tes fo esoht stnemele fo ELPMAXE
)6.1-11( A rof hcihw eht EX( R xI )5<
noitisoporp )x(p si eurt fI ti si raelc from eht txetnoc hcihw tes A
si gnieb ,deredisnoc eht noitaton
nac eb .desu
{X [p(x))
ELPMAXE
x{ xI < 5)
1 7.4-l drac drac (A) rebmun fo stnemele ni A;
(-1 lanidrac fo A
8.4-11 0 eht ytpme tes
(7 )7.1-l

9.4-11 N N eht tes fo larutan N = ,0( ,3,2,1 ...)
;srebmun noisulcxE fo orez from eht stes 1 9.4-l
(11-1.8)
eht tes fo evitisop ot 31.4-11 si detoned yb na asterisk,
sregetni dna orez .g.e .*VI
=,N ,0( ,1 . ...k- }I
01.4-11 Z z eht tes fo sregetni E = ,...( ,2- ,1- ,0 ,1 ,2 ...)
(1 )9.1-I eeS remark ot 1 .9.4-l
11.4-11 Q 0 eht tes fo lanoitar eeS remark ot .9.4-11
I( .7-l )OI srebmun
21.4-11 R R eht tes fo laer srebmun eeS remark ot 1 .9.4-l
)11.1-11(
31.4-11 C c eht tes fo xelpmoc eeS remark ot 1 .9.4-l
I( .l-l )21 srebmun
3
IS 1890 (Part 11) : 1995
IS0 31-11 : 1992
4 SETS deunitnoc(
Symbol,
Item No. Application Meaning, verbal equivalent Remarks and examples
sign
11-4.14 [ ,] CR bl desolc interval ni R morf a ,a[ b] = (x E R I a G x d bj
(4 )dedulcni( ot b )dedulcni(
51.4-11 ] ], 1~ bl tfel nepo-flah lavretni ni R ,a] b] = (x E R 1a < x < b)
k-4 (,I (0. lb morf a )dedulcxe( ot b
)dedulcni(
61.4-11 [ , [ .uC 4 thgir nepo-flah lavretni ni R ,a[ b[ = {x E R I a d x c b}
(-4 [I) Cat b) morf a )dedulcni( ot b
)dedulcxe(
71.4-11 ,1 [ la bC nepo lavretni ni R morf a ,a] b[ = (x E R 1a < x < b}
(4 (, 1 (at b) )dedulcxe( ot b )dedulcxe(
81.4-11 E BEA B is dedulcni ni A; yrevE tnemele fo B sgnoleb ot A.
(1 l-l. 13) B is a tesbus fo A c is osla ,desu tub ees kramer ot ? .91.4-1
91.4-11 c BcA B is ylreporp dedulcni ni A; yrevE tnemele fo B sgnoleb ot A, tub B SI
[ 1 .l-l )41 B is a reporp tesbus fo A ton lauqe ot A.
If c is desu rof ,81.4-11 neht s llahs eb
desu rof .91.4-11
02.4-11 $ A$C C is ton dedulcni ni A; q is osla .desu
)51.1-11( C is ton a tesbus fo A ehT slobmys Q dna Q era osla .desu
12.4-11 2 AzB A sedulcni B sa( )tesbus A sniatnoc yreve tnemele fo B.
(II-?. 76) 3 is osla ,desu tub ees kramer ot 1 .22.4-l
A =, B sah eht emas gninaem sa B c A.

1 22.4-l IJ AI>B A sedulcni B ylreporp A sniatnoc yreve tnemele fo B, tub A is
.l-11( )71 ton lauqe ot B.
If 2 is desu rof ,12.4-11 neht 2 llahs eb
desu rof .22.4-11
A 3 B sah eht emas gninaem sa B c A.
32.4-11 ?$ AZC A seod ton edulcni C sa( P is osla .desu
I( )81.1-1 )tesbus ehT slobmys p dna $ era osla .desu
A 8 C sah eht emas gninaem sa C $ A.
42.4-11 u AuB noinu fo A dna B ehT tes fo stnemele hcihw gnoleb ot A
(I l-1.79) ro ot B ro ot htob A dna .B
AIJB={~~xEAv~EB)
4
IS 1890 (Part 11) : 1995
IS0 31-11 : 1992
4 SETS (continued
Symbol,
Item No. Application Meaning, verbal equivalent Remarks and examples
sign
11-4.25 U L.YAJi union of a collection of sets 6 Ai = A, u A, u . . . w A,,
(7 7-1.20 i=l i=l
A,, . ..t A,
eht tes fo elements belonging to at least
one of the sets A,, . . . . A,.
Ul= I dna iv,1 Ui lE
era osla ,desu where I denotes a set of
indices.
11-4.26 n AnB noitcesretni fo A dna B, ehT tes fo stnemele hcihw gnoleb ot htob
)12.1-71( daer sa A retni B A dna B.
AnB=(xlxEA~xcB)
72.4-11 n ir ,A noitcesretni fo a noitcelloc ,,An...n,An,A=iA)!!f
I( )22.1-1 i=l fo stes A,, . . . . A,, i=l
eht tes fo stnemele gnignoleb ot lla stes
A,, A,, . . . dna A,,.
era osla ,desu erehw* I setoned a tes fo
.secidni
82.4-11 B\A ecnereffid neewteb A dna ehT tes fo stnemele hcihw gnoleb ot A,
(1 )32.1-I ;B tub ton ot B.
A sunim B A\B= (xIx~Ar\x#B)
A -B dluohs ton eb .desu

92.4-11 c BL tnemelpmoc fo tesbus B ehT tes fo esoht stnemele fo A hcihw od
(I )42.1-l fo A ton gnoleb ot eht tesbus B.
fI ti si raelc from eht txetnoc hcihw tes A
si gnieb ,deredisnoc eht lobmys A si netfo
.dettimo
oslA CAB = A \ B
03.4-11 (,) ,a( b) deredro riap a, b; (a, b) = (c, d) fi dna ylno fi a = c dna
1I J52.1-I elpuoc a, b b = d.
(a, b) si osla .desu
13.4-11 ( , . . . . ) ,,a( ,,a . . . . ),a deredro telput-n (a,, %, . . . . a,) si osla .desu
[ )62.1-ll

5