EN ISO 80000-2:2013
(Main)Quantities and units - Part 2: Mathematical signs and symbols to be used in the natural sciences and technology (ISO 80000-2:2009)
Quantities and units - Part 2: Mathematical signs and symbols to be used in the natural sciences and technology (ISO 80000-2:2009)
ISO 80000-2:2009 gives general information about mathematical signs and symbols, their meanings, verbal equivalents and applications.
The recommendations in ISO 80000-2:2009 are intended mainly for use in the natural sciences and technology, but also apply to other areas where mathematics is used.
Größen und Einheiten - Teil 2: Mathematische Zeichen für Naturwissenschaft und Technik (ISO 80000-2:2009)
ISO 80000-2 stellt allgemeine Angaben zu mathematischen Zeichen, deren Bedeutung, Sprechweise und Anwendung bereit.
Die Empfehlungen in ISO 80000-2 richten sich hauptsächlich an Naturwissenschaft und Technik, sind jedoch auch in anderen Bereichen anwendbar, in denen Mathematik verwendet wird.
Grandeurs et unités - Partie 2: Signes et symboles mathématiques à employer dans les sciences de la nature et dans la technique (ISO 80000-2:2009)
L'ISO 80000-2:2009 donne des informations générales sur les signes et symboles mathématiques, leurs sens, leurs énoncés et leurs applications.
Les recommandations données dans l'ISO 80000-2:2009 sont principalement destinées à être utilisées dans les sciences de la nature et dans la technique. Cependant, elles s'appliquent également à d'autres domaines utilisant les mathématiques.
Veličine in enote - 2. del: Matematični znaki in simboli za uporabo v naravoslovnih vedah in tehniki (ISO 80000-2:2009)
Standard ISO 80000-2:2009 podaja splošne informacije o matematičnih znakih in simbolih, njihovem pomenu, besednih ekvivalentih in uporabi. Priporočila v standardu ISO 80000-2:2009 so namenjena zlasti uporabi v naravoslovnih vedah in tehniki, vendar se uporabljajo tudi na drugih področjih, kjer se uporablja matematika.
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2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Größen und Einheiten - Teil 2: Mathematische Zeichen für Naturwissenschaft und Technik (ISO 80000-2:2009)Grandeurs et unités - Partie 2: Signes et symboles mathématiques à employer dans les sciences de la nature et dans la technique (ISO 80000-2:2009)Quantities and units - Part 2: Mathematical signs and symbols to be used in the natural sciences and technology (ISO 80000-2:2009)07.020MatematikaMathematics01.075Simboli za znakeCharacter symbols01.060Quantities and unitsICS:Ta slovenski standard je istoveten z:EN ISO 80000-2:2013SIST EN ISO 80000-2:2013en01-junij-2013SIST EN ISO 80000-2:2013SLOVENSKI
STANDARDSIST ISO 31-11:1995SIST ISO 31-11:19951DGRPHãþD
EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE 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 unités - Partie 2: Signes et symboles mathématiques à employer dans les sciences de la nature et dans la technique (ISO 80000-2:2009)
Größen und Einheiten - Teil 2: Mathematische Zeichen für Naturwissenschaft und Technik (ISO 80000-2:2009) This European Standard was approved by CEN on 14 March 2013.
CEN members are 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 the 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 Centre 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, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.
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Reference numberISO 80000-2:2009(E)© ISO 2009
INTERNATIONAL STANDARD ISO80000-2First edition2009-12-01Quantities and units — Part 2: Mathematical signs and symbols to be used in the natural sciences and technology Grandeurs et unités — Partie 2: Signes et symboles mathématiques à employer dans les sciences de la nature et dans la technique
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ii © ISO 2009 – All rights reserved
ISO 80000-2:2009(E) © ISO 2009 – All rights reserved iii Contents Page Foreword.iv Introduction.vi 1 Scope.1 2 Normative references.1 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 8 Elementary geometry.10 9 Operations.11 10 Combinatorics.14 11 Functions.15 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.31 Annex A (normative)
Clarification of the symbols used.36 Bibliography.40
ISO 80000-2:2009(E) iv © ISO 2009 – All rights reserved Foreword 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 subject 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 (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 committees 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 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 major 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: General ⎯ 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 numbers ⎯ Part 12: Solid state physics
1) Title to be shortened to read “Mathematics” in the second edition of ISO 80000-2. SIST EN ISO 80000-2:2013
ISO 80000-2:2009(E) © ISO 2009 – All rights reserved v IEC 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 80000-2:2009(E) vi © ISO 2009 – All rights reserved 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 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 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. 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 mathematically complete. The arrangement of the table in Clause 16 “Coordinate systems” is somewhat different.
INTERNATIONAL STANDARD ISO 80000-2:2009(E) © ISO 2009 – All rights reserved 1 Quantities 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 recommendations 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 edition 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 Σi xi are printed in italic (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) type, e.g. sin, exp, ln, Γ. Mathematical constants, the values of which never change, are printed in Roman (upright) type, e.g. e = 2,718 218 8…; π = 3,141 592…; i2 =
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