DIN EN ISO 80000-2-2013 Quantities and units - Part 2 Mathematical signs and symbols to be used in the natural sciences and technology (ISO 80000-2 2009) German version EN ISO 8000.pdf

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1、August 2013 Translation by DIN-Sprachendienst.English price group 17No part of this translation may be reproduced without prior permission ofDIN Deutsches Institut fr Normung e. V., Berlin. Beuth Verlag GmbH, 10772 Berlin, Germany,has the exclusive right of sale for German Standards (DIN-Normen).ICS

2、 01.075; 01.060!%(|“2052789www.din.deDDIN EN ISO 80000-2Quantities and units Part 2: Mathematical signs and symbols to be used in the naturalsciences and technology (ISO 80000-2:2009);English version EN ISO 80000-2:2013,English translation of DIN EN ISO 80000-2:2013-08Gren und Einheiten Teil 2: Math

3、ematische Zeichen fr Naturwissenschaft und Technik (ISO 80000-2:2009);Englische Fassung EN ISO 80000-2:2013,Englische bersetzung von DIN EN ISO 80000-2:2013-08Grandeurs et units Partie 2: Signes et symboles mathmatiques employer dans les sciences de la nature etdans la technique (ISO 80000-2:2009);V

4、ersion anglaise EN ISO 80000-2:2013,Traduction anglaise de DIN EN ISO 80000-2:2013-08www.beuth.deDocument comprises 8 pagesIn case of doubt, the German-language original shall be considered authoritative.408.13 DIN EN ISO 80000-2:2013-08 2 A comma is used as the decimal marker. National foreword The

5、 text of ISO 80000-2:2009 has been prepared by Technical Committee ISO/TC 12 “Quantities and units” (Secretariat: SIS, Sweden) and has been taken over as EN ISO 80000-2:2013 by the CEN Technical Board (BT). The responsible German body involved in its preparation was the Normenausschuss Technische Gr

6、undlagen (Fundamental Technical Standards Committee), Working Group NA 152-01-02-01 AK Mathematische Begriffe und Zeichen. ISO 80000 consists of the following parts, under the general title Quantities and units: Part 1: General Part 2: Mathematical signs and symbols to be used in the natural science

7、s and technology) 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 numbers Part 12: Solid state physics IEC 80000 consists of the following part

8、s, under the general title Quantities and units: Part 6: Electromagnetism Part 13: Information science and technology Part 14: Telebiometrics related to human physiology The DIN Standards corresponding to the International Standards referred to in Clause 2 and in the Bibliography of this document ar

9、e as follows: ISO 80000-1 DIN EN ISO 80000-1 IEC 60027-6 DIN EN 60027-6 Notes to the German version of this standard and on deviations from usage in German-speaking areas Re Clause 3 The number e is incorrectly given as ., 82187182 . In this German version this has been correctly given as ., 8281718

10、2 . Re 2-9.5 Writing a product in the form ab without any spaces is against the rule set down in DIN 1338, according to which the factors of a product are to have at least one space (of a defined length) between them. According to DIN 1338 and German school curricula, the multiplication sign (cross)

11、 is only to be used to indicate vector products and formats (such as paper sizes), but not for the multiplication of scalar quantities such as numbers. In Germany, the dot as a multiplication sign is to be used for indicating the multiplication of scalar quantities. )The title of the second edition

12、of ISO 80000-2 will be shortened to read Mathematics. DIN EN ISO 80000-2:2013-08 3 National Annex NA (informative) Bibliography DIN 1302, General mathematical symbols and concepts DIN 1303, Vectors, matrices, tensors Symbols and concepts DIN 1312, Geometrical Orientation DIN 1333, Presentation of nu

13、merical data DIN 4895-1, Orthogonal coordinate systems General concepts DIN 4895-2, Orthogonal coordinate systems Differential operators of vector analysis DIN 5473, Logic and set theory Symbols and concepts DIN 5477, Per cent, parts per thousand Concepts, use DIN 13302, Mathematical structures Sign

14、s, symbols and concepts DIN EN 60027-6, Letter symbols to be used in electrical technology Part 6: Control technology DIN EN 80000-6, Quantities and units Part 6: Electromagnetism DIN EN 80000-13, Quantities and units Part 13: Information science and technology DIN EN 80000-14, Quantities and units

15、Part 14: Telebiometrics related to human physiology DIN EN ISO 80000-1, Quantities and units Part 1: General DIN EN ISO 80000-2, Quantities and units Part 2: Mathematical signs and symbols to be used in the natural sciences and technology DIN EN ISO 80000-3, Quantities and units Part 3: Space and ti

16、me DIN EN ISO 80000-4, Quantities and units Part 4: Mechanics DIN EN ISO 80000-5, Quantities and units Part 5: Thermodynamics DIN EN ISO 80000-7), Quantities and units Part 7: Light DIN EN ISO 80000-8, Quantities and units Part 8: Acoustics DIN EN ISO 80000-9, Quantities and units Part 9: Physical c

17、hemistry and molecular physics DIN EN ISO 80000-10, Quantities and units Part 10: Atomic and nuclear physics DIN EN ISO 80000-11, Quantities and units Part 11: Characteristic numbers DIN EN ISO 80000-12, Quantities and units Part 12: Solid state physics )In preparation. DIN EN ISO 80000-2:2013-08 4

18、This page is intentionally blank 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 - Partie 2: Sig

19、nes 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 and CENELEC members are

20、 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

21、he CEN-CENELEC Management Centre or to any CEN and CENELEC 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 and CENELEC member into its own language and notified to the CE

22、N-CENELEC Management Centre has the same status as the official versions. CEN and CENELEC members are the national standards bodies and national electrotechnical committees of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedoni

23、a, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom. CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels 2013 CEN/CEN

24、ELEC All rights of exploitation in any form and by any means reserved worldwide for CEN national Members and for CENELEC Members. Ref. No. EN 80000-2:2013 E Contents EN ISO 80000-2:2013 (E) DIN EN ISO 80000-2:2013-08 2 Page Foreword 3 Introduction .4 1 Scope 5 2 Normative references 5 3 Variables, f

25、unctions, and operators.5 4 Mathematical logic .7 5 Sets .8 6 Standard number sets and intervals 10 7 Miscellaneous signs and symbols .12 8 Elementary geometry 14 9 Operations 15 10 Combinatorics 18 11 Functions 19 12 Exponential and logarithmic functions .22 13 Circular and hyperbolic functions .23

26、 14 Complex numbers25 15 Matrices 26 16 Coordinate systems 28 17 Scalars vectors, and tensors 30 18 Transforms .34 19 Special functions .35 Annex A (normative) Clarification of the symbols used .40 Bibliography 44 Foreword The text of ISO 80000-2:2009 has been prepared by Technical Committee ISO/TC

27、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 standard, either by publication of an identical text or by endorsement, at the latest by October 2013,

28、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. CEN and/or CENELEC shall not be held responsible for identifying any or all such patent rights. A

29、ccording 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, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germ

30、any, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom. Endorsement notice The text of ISO 80000-2:2009 has been approved by CEN as EN ISO 80000

31、-2:2013 without any modification. EN ISO 80000-2:2013 (E) DIN EN ISO 80000-2:2013-08 3 Introduction Arrangement of the tables The first column “Item No.” of the tables 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

32、 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 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

33、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 expression may be read. This is for the identification of the concept and is not intended to be a complete mathematical definition. T

34、he 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 mathematically complete. The arrangement of the table in Clause 16 “Coordinate systems” is somewhat different. EN ISO 80000-2:2013 (E) DIN

35、 EN ISO 80000-2:2013-08 4 1 Scope ISO 80000-2 gives general information about mathematical signs and symbols, their meanings, verbal equivalents and applications. The recommendations in ISO 80000-2 are intended mainly for use in the natural sciences and technology, but also apply to other areas wher

36、e mathematics is used. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO

37、 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 italic (sloping) type. Parameters, such as a, b, etc., which may be considered as constant in a particular context, are printed in

38、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) type, e.g. sin, exp, ln, . Mathematical constants, the values of which never change, are printed in Roman (upright) type, st

39、yle, e.g. div, in x and each d in df/dx. Numbers expressed in the form of 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 f

40、irst parenthesis, e.g. f(x), cos(t + ). If the symbol for the function consists 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 func

41、tion and the argument, e.g. int 2,4; sin n; arcosh 2A; Ei x. If there is 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) EN ISO 80000-2:2013 (E

42、) e.g. e 2,718 218 8N1); 3,141 592; i2 1. Well-defined operators are also printed in Roman (upright) N1) National footnote: See explanatory notes Re Clause 3 in the National foreword “Notes to the German version of this standard and on deviations from usage in German-speaking areas”. DIN EN ISO 8000

43、0-2:2013-08 5 A comma, semicolon or other appropriate symbol can be used as a separator between numbers or expressions. The comma is generally 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

44、 shall be used. a) Place the line breaks immediately after one of the symbols =, +, , or , or, if necessary, immediately after one of the 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

45、of the symbols =, +, , or , or, if necessary, immediately before one of the symbols , , or /. In this case, the symbol indicates that the 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

46、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 expression 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

47、appropriate context. There are no strict rules for the use of letter fonts which should, however, be explained if necessary. EN ISO 80000-2:2013 (E) DIN EN ISO 80000-2:2013-08 6 4 Mathematical logic Item No. Sign, symbol, expression Meaning, verbal equivalent Remarks and examples 2-4.1 (11-3.1) p q

48、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) p negation of p, not p 2-4.4 (11-3.4) p q p implies q, if p, then q q p has the same meaning as p q. is the implication symbol. 2-4.5 (11-3.5) p q p is equivalent to q (p q) (q p) has the same meaning as p q. is the equivalence symbol.