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Ref. No.: ISO/R3l/Part XI - l%l (E)
IS0
IN TERN AT1 ON AL ORGAN IZATl O N FOR STAND A RD IZATl ON
IS0 RECOMMENDATION
O
R 31
PART XI
MATHEMATICAL SIGNS AND SYMBOLS
FOR USE IN PHYSICAL SCIENCES AND TECHNOLOGY
1st EDITION
February 1961
O
COPY RIGHT RESERVED
The copyri&.t of IS0 Recommendations and IS Standards
belongs to IS0 Member Bodies. Reproduction of these
documents, in any country, may be authorized therefore only
by the national standards organization of that country, being
a member of 1S0.
For each individual country the only valid standard is the national standard of that country.
Printed in Denmark
Also issued in French and Russian. Copies to be obtained through the national standards organizations.
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BRIEF HISTORY
The IS0 Recommendation R 31, Part XI, Mathematiccil Signs nnd Syntbols for Use
in the Physical Sciences and Technology, was chu n ul) hy T(hcIini(*al Committee
lSO/'I'C 12, Quantities, Units, Symbols, Conversion Factors and Conversion Tables,
the Secretariat of which is held by the Danish Standards Association, l)arl\k
Standartliscriiigsr~tl (1)s).
The ISO/'l'C 12 Secretariat drew up two drafts in succession, the second of \\-hicIl
was studied by the Technical Committee during its fourth meeting, held in Copen-
hagen in November 1957. The Secretariat then prepared a third draft proposal,
which \\.as submitted by correspondence to the Members of thc Tech~~ical Com-
mittee and was approved as a Draft IS0 I\ecomment€ation.
It should be noted that the following international organizations have had these
draft proposals sent to theni and have taken part in the cliscussions at the meetings
of Technical Committee lSO/TC 12:
International Commission on Illumination
Iiitcrnutional Committee on Weights and lleasnrcs
International Electrotechnical Commission
International Union of Pure and Applied Chemistry
International Union of Pure and Applied Physics
and its Sub-Committee SUN
Organisation Internationale de Métrologie IAgale.
On 29 May 1959, the Draft IS0 Recommendation (No. 287) ivas (listributcd to all
the IS0 Member Bodies and was approved by the follo\ving LIcmbc~r Is:
Australia Grei!ce Poland
Hungary
Austria Portugal
Belgium India Romani:{
Burma Ireland Spain
Canad a .J a pa ri S\vcden
Chile Netherlands S i t z er1 a n (1
1)enmark New Zealand U. S.A.
France xor\vny r. s. s. I\.
1% liistan
Germany
'I'hrce Mrmhcr I3otlic's opposed thc approval of thc Draft:
('zecliodo\.altia, Italv, United Kingdom.
The Draft IS0 Rcco1iinieiit1:ition n as then suhmittetl by correspondence to the IS0
Council, \vhich ctecitlcd, ill Fehruary 1961, to :ic~c~pt it as an IS0 l~FXO~lhIl DATI ON.
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lSO/R 31 /Part XI- 1961 (E)
Mathematical Signs and Symbols for Use
in the Physical Sciences and Technology
Introduction
‘l’hi<, docuiiicnf, contaiiiilig a selection of inntheninlicnl si!yiis niid syiirbols recommended for use in the phy-
sical scicncrs and tcrlrnology, is part of a morc comprehensive publication dealing with quantities and units
on various lielcls of science ant1 teclinology.
This puhlication i\ iqcucd a\ IS0 RecommendatioI1~atio~i H 3l/l’art I, l’ait II, etc.
\\’here sevc~.al signs or symhols \\ it11 the same meaning are given, they arc on an equal footing.
So reconiinendntioii i\ madc or implied ahout the fount of upright type in which certain mathematical symbols
are printed. In (I:is docuincnt thc same fount is used as in the roloinns 6c,lleaning” and “Rcmarhs”.
Some principles for printing synil~ols and numhcrs arc given in IS0 Recomnientlation R 31 /Part XII e)
1. Arithmetic, algebra and analysis of real scalar quantities
Item
Remarks
Sign or Symbol Meaning
No.
-
1 .l equal to
not equal to
1.2
identically equal to It is recommended not to use this sign with
1.3
the meaning “defined as equal to”.
Examples:
corresponds to
1.4
On the basis of the equation E=rncz,
9 x 10’O erg
1 g
C
When 1 cm on a map corresponds to a length
of 10 km one may write 1 cm ~10 km
approximately equal to
1.5
approaches
1.6
- is also used
asymptotically equal to
1.7
CL is also used
proportional to
1.8
infinity
1.9
smaller than
1.10
larger than
1.11
smaller than or equal to
1.12
larger than or equal to
1.13
much smaller than
1.14
much larger than
1.15
plus
1.16
*) Draft IS0 Recommendation No. 345
-3-
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lSO/R 31/Part XI - 1961 (E)
-
Item
Sign or Symbol
Meaning
Remarks
No.
-
-
1.17
minus
1.18
'X. mu1 ti plied by
1.19 a divided by b'
a: b is also used
1.20 magnitude of a
1.21 a raised to the power n
1.22 square root of a
When the sign 4 or d is to operate on a
composite expression, brackets should be
used.
1.23
n'th root of a
1.24
mean value of U
The meaning of "mean value" is not comple-
tely defined until the averaging procedure is
specified.
1.25
factorial p, 1 x 2x 3 x . . . xp
P! p is a positive integer
n (n - 1) . . . (n - p + 1)
binomial coefficient.
1.26
.I x 2 x ,. x p
1.27
sum
product
i .2a
f (or f) of the variable x
1.29 fun
...