BS EN ISO 80000-2-2013 Quantities and units Mathematical signs and symbols to be used in the natural sciences and technology《数量和单位 自然科学和技术中使用的数学标志与符号》.pdf

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1、BS EN ISO80000-2:2013ICS 01.060NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWBRITISH STANDARDQuantities and unitsPart 2: Mathematical signs andsymbols to be used in the naturalsciences and technologyCopyright European Committee for Standardization Provided by IHS under licens

2、e with CENNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-National forewordThis British Standard is the UK implementation of EN ISO 80000-2:2013. It supersedes BS ISO 80000-2:2009, which is withdrawn.The UK participation in its preparation was entrusted to Technica

3、l Committee SS/7, General metrology, quantities, units and symbols.A list of organizations represented on this committee can be obtained on request to its secretary.This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct applicat

4、ion.Compliance with a British Standard cannot confer immunity from legal obligations.BS EN ISO 80000-2:2013This British Standard was published under the authority of the Standards Policy and Strategy Committee on 31 January 2010 The British Standards Institution 2013. Published by BSI Standards Limi

5、ted 2013Amendments/corrigenda issued since publicationDate Comments 31 May 2013 This corrigendum renumbers BS ISO 80000-2:2009 as BS EN ISO 80000-2:2013ISBN 978 0 580 79018 8Copyright European Committee for Standardization Provided by IHS under license with CENNot for ResaleNo reproduction or networ

6、king permitted without license from IHS-,-,-EUROPEAN STANDARD NORME EUROPENNE EUROPISCHE NORM EN ISO 80000-2 April 2013 ICS 01.060 English Version Quantities and units - Part 2: Mathematical signs and symbols to be used in the natural sciences and technology (ISO 80000-2:2009) Grandeurs et units - P

7、artie 2: Signes et symboles mathmatiques employer dans les sciences de la nature et dans la technique (ISO 80000-2:2009) Gren und Einheiten - Teil 2: Mathematische Zeichen fr Naturwissenschaft und Technik (ISO 80000-2:2009) This European Standard was approved by CEN on 14 March 2013. CEN members are

8、 bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to t

9、he CEN-CENELEC Management Centre or to any CEN member. This European Standard exists in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Cen

10、tre has the same status as the official versions. CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuan

11、ia, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom. EUROPEAN COMMITTEE FOR STANDARDIZATION COMIT EUROPEN DE NORMALISATION EUROPISCHES KOMITEE FR NORMUNG Management Centre: Avenue Marnix 17, B-1000 Brussels

12、2013 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN ISO 80000-2:2013: ECopyright European Committee for Standardization Provided by IHS under license with CENNot for ResaleNo reproduction or networking permitted without license fr

13、om IHS-,-,-Foreword The text of ISO 80000-2:2009 has been prepared by Technical Committee ISO/TC 12 “Quantities and units” of the International Organization for Standardization (ISO) and has been taken over as EN ISO 80000-2:2013. This European Standard shall be given the status of a national standa

14、rd, either by publication of an identical text or by endorsement, at the latest by October 2013, and conflicting national standards shall be withdrawn at the latest by October 2013. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights.

15、CEN and/or CENELEC shall not be held responsible for identifying any or all such patent rights. According to the CEN-CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cypru

16、s, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United

17、Kingdom. Endorsement notice The text of ISO 80000-2:2009 has been approved by CEN as EN ISO 80000-2:2013 without any modification. BS EN ISO 80000-2:2013 ISO 80000-2:2013 (E)EN Copyright European Committee for Standardization Provided by IHS under license with CENNot for ResaleNo reproduction or net

18、working permitted without license from IHS-,-,- ISO 20 All rights reserved iiiContents Page Foreword iv Introductionvi 1 Scope1 2 Normative references1 3 Variables, functions, and operators 1 4 Mathematical logic 3 5 Sets .4 6 Standard number sets and intervals .6 7 Miscellaneous signs and symbols 8

19、 8 Elementary geometry10 9 Operations11 10 Combinatorics .14 11 Functions15 12 Exponential and logarithmic functions .18 13 Circular and hyperbolic functions .19 14 Complex numbers .21 15 Matrices 22 16 Coordinate systems 24 17 Scalars, vectors, and tensors 26 18 Transforms.30 19 Special functions.3

20、1 Annex A (normative) Clarification of the symbols used.36 Bibliography40 13BS EN ISO 80000-2:2013 ISO 80000-2:2009 (E)Copyright European Committee for Standardization Provided by IHS under license with CENNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-iv ISO 2013

21、 All rights reservedForeword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing International Standards is normally carried out through ISO technical committees. Each member body interested in a s

22、ubject for which a technical committee has been established has the right to be represented on that committee. International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical Commission

23、(IEC) on all matters of electrotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2. The main task of technical committees is to prepare International Standards. Draft International Standards adopted by the technical comm

24、ittees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. ISO shall not

25、be held responsible for identifying any or all such patent rights. ISO 80000-2 was prepared by Technical Committee ISO/TC 12, Quantities and units, in collaboration with IEC/TC 25, Quantities and units. This first edition cancels and replaces ISO 31-11:1992, which has been technically revised. The m

26、ajor technical changes from the previous standard are the following: Four clauses have been added, i.e. “Standard number sets and intervals”, “Elementary geometry”, “Combinatorics” and “Transforms”. ISO 80000 consists of the following parts, under the general title Quantities and units: Part 1: Gene

27、ral Part 2: Mathematical signs and symbols to be used in the natural sciences and technology1) Part 3: Space and time Part 4: Mechanics Part 5: Thermodynamics Part 7: Light Part 8: Acoustics Part 9: Physical chemistry and molecular physics Part 10: Atomic and nuclear physics Part 11: Characteristic

28、numbers Part 12: Solid state physics 1) Title to be shortened to read “Mathematics” in the second edition of ISO 80000-2. BS EN ISO 80000-2:2013 ISO 80000-2:2009 (E)Copyright European Committee for Standardization Provided by IHS under license with CENNot for ResaleNo reproduction or networking perm

29、itted without license from IHS-,-,-vIEC 80000 consists of the following parts, under the general title Quantities and units: Part 6: Electromagnetism Part 13: Information science and technology Part 14: Telebiometrics related to human physiology ISO 20 All rights reserved 13BS EN ISO 80000-2:2013 IS

30、O 80000-2:2009 (E)Copyright European Committee for Standardization Provided by IHS under license with CENNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-vi ISO 2013 All rights reservedIntroduction Arrangement of the tables The first column “Item No.” of the tables

31、contains the number of the item, followed by either the number of the corresponding item in ISO 31-11 in parentheses, or a dash when the item in question did not appear in ISO 31-11. The second column “Sign, symbol, expression” gives the sign or symbol under consideration, usually in the context of

32、a typical expression. If more than one sign, symbol or expression is given for the same item, they are on an equal footing. In some cases, e.g. for exponentiation, there is only a typical expression and no symbol. The third column “Meaning, verbal equivalent” gives a hint on the meaning or how the e

33、xpression may be read. This is for the identification of the concept and is not intended to be a complete mathematical definition. The fourth column “Remarks and examples” gives further information. Definitions are given if they are short enough to fit into the column. Definitions need not be mathem

34、atically complete. The arrangement of the table in Clause 16 “Coordinate systems” is somewhat different. BS EN ISO 80000-2:2013 ISO 80000-2:2009 (E)Copyright European Committee for Standardization Provided by IHS under license with CENNot for ResaleNo reproduction or networking permitted without lic

35、ense from IHS-,-,-INTERNATIONAL STANDARD 1Quantities and units Part 2: Mathematical signs and symbols to be used in the natural sciences and technology 1 Scope ISO 80000-2 gives general information about mathematical signs and symbols, their meanings, verbal equivalents and applications. The recomme

36、ndations in ISO 80000-2 are intended mainly for use in the natural sciences and technology, but also apply to other areas where mathematics is used. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the editio

37、n cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO 80000-1:2), Quantities and units Part 1: General 3 Variables, functions and operators Variables such as x, y, etc., and running numbers, such as i in ixiare printed in itali

38、c (sloping) type. Parameters, such as a, b, etc., which may be considered as constant in a particular context, are printed in italic (sloping) type. The same applies to functions in general, e.g. f, g. An explicitly defined function not depending on the context is, however, printed in Roman (upright

39、) type, e.g. sin, exp, ln, . Mathematical constants, the values of which never change, are printed in Roman (upright) type, e.g. e = 2,718 218 8; = 3,141 592; i2= 1. Well-defined operators are also printed in Roman (upright) style, e.g. div, in x and each d in df/dx. Numbers expressed in the form of

40、 digits are always printed in Roman (upright) style, e.g. 351 204; 1,32; 7/8. The argument of a function is written in parentheses after the symbol for the function, without a space between the symbol for the function and the first parenthesis, e.g. f(x), cos(t + ). If the symbol for the function co

41、nsists of two or more letters and the argument contains no operation symbol, such as +, , , or / , the parentheses around the argument may be omitted. In these cases, there should be a thin space between the symbol for the function and the argument, e.g. int 2,4; sin n; arcosh 2A; Ei x. If there is

42、any risk of confusion, parentheses should always be inserted. For example, write cos(x) + y; do not write cos x + y, which could be mistaken for cos(x + y). 2) To be published. (Revision of ISO 31-0:1992) ISO 20 All rights reserved13BS EN ISO 80000-2:2013 ISO 80000-2:2009 (E)Copyright European Commi

43、ttee for Standardization Provided by IHS under license with CENNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 ISO 2013 All rights reservedA comma, semicolon or other appropriate symbol can be used as a separator between numbers or expressions. The comma is gener

44、ally preferred, except when numbers with a decimal comma are used. If an expression or equation must be split into two or more lines, one of the following methods shall be used. a) Place the line breaks immediately after one of the symbols =, +, , or , or, if necessary, immediately after one of the

45、symbols , , or /. In this case, the symbol indicates that the expression continues on the next line or next page. b) Place the line breaks immediately before one of the symbols =, +, , or , or, if necessary, immediately before one of the symbols , , or /. In this case, the symbol indicates that the

46、expression is a continuation of the previous line or page. The symbol shall not be given twice around the line break; two minus signs could for example give rise to sign errors. Only one of these methods should be used in one document. If possible, the line break should not be inside of an expressio

47、n in parentheses. It is customary to use different sorts of letters for different sorts of entities. This makes formulas more readable and helps in setting up an appropriate context. There are no strict rules for the use of letter fonts which should, however, be explained if necessary. BS EN ISO 800

48、00-2:2013 ISO 80000-2:2009 (E)Copyright European Committee for Standardization Provided by IHS under license with CENNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-34 Mathematical logic Item No. Sign, symbol, expression Meaning, verbal equivalent Remarks and examples 2-4.1 (11-3.1) p q conjunction of p and q, p and q 2-4.2 (11-3.2) p q disjunction of p and q, p or q This “or” is inclusive, i.e. p q is true, if either p or q, or both are true. 2-4.3 (11-3.3)