# EN ISO 80000-2:2019

(Main)## Quantities and units - Part 2: Mathematics (ISO 80000-2:2019, Corrected version 2021-11)

## Quantities and units - Part 2: Mathematics (ISO 80000-2:2019, Corrected version 2021-11)

This document specifies mathematical symbols, explains their meanings, and gives verbal equivalents and applications.

This document is intended mainly for use in the natural sciences and technology, but also applies to other areas where mathematics is used.

## Größen und Einheiten - Teil 2: Mathematik (ISO 80000-2:2019, korrigierte Fassung 2021-11)

Dieses Dokument legt mathematische Zeichen fest, erläutert deren Bedeutung und gibt Sprechweise und Anwendungen an.

Dieses Dokument richtet sich hauptsächlich an Naturwissenschaft und Technik, ist jedoch auch in anderen Bereichen anwendbar, in denen Mathematik verwendet wird.

## Grandeurs et unités - Partie 2: Mathématiques (ISO 80000-2:2019, Version corrigée 2021-11)

Le présent document spécifie les symboles mathématiques, explique leurs sens et donne leurs énoncés et leurs applications.

Le présent document est principalement destiné à être utilisé dans les sciences de la nature et dans la technique. Cependant, il s'applique également à d'autres domaines utilisant les mathématiques.

## Veličine in enote - 2. del: Matematika (ISO 80000-2:2019)

Ta dokument določa matematične simbole in razlaga njihov pomen ter podaja besedne ustreznice in načine uporabe. Ta dokument je namenjen zlasti uporabi v naravoslovnih vedah in tehniki, vendar se uporablja tudi na drugih področjih, kjer se uporablja matematika.

### General Information

### RELATIONS

### Standards Content (sample)

SLOVENSKI STANDARD

SIST EN ISO 80000-2:2019

01-december-2019

Nadomešča:

SIST EN ISO 80000-2:2013

Veličine in enote - 2. del: Matematika (ISO 80000-2:2019)

Quantities and units - Part 2: Mathematics (ISO 80000-2:2019)

Größen und Einheiten - Teil 2: Mathematik (ISO 80000-2:2019)

Grandeurs et unités - Partie 2: Mathématiques (ISO 80000-2:2019)

Ta slovenski standard je istoveten z: EN ISO 80000-2:2019

ICS:

01.060 Veličine in enote Quantities and units

07.020 Matematika Mathematics

SIST EN ISO 80000-2:2019 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 80000-2:2019

EN ISO 80000-2

EUROPEAN STANDARD

NORME EUROPÉENNE

October 2019

EUROPÄISCHE NORM

ICS 01.060; 01.075 Supersedes EN ISO 80000-2:2013

English Version

Quantities and units - Part 2: Mathematics (ISO 80000-

2:2019)

Grandeurs et unités - Partie 2: Mathématiques (ISO Größen und Einheiten - Teil 2: Mathematik (ISO 80000-

80000-2:2019) 2:2019)This European Standard was approved by CEN on 5 May 2019.

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, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,

Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and

United Kingdom.EUROPEAN COMMITTEE FOR STANDARDIZATION

COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels

© 2019 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 80000-2:2019 E

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SIST EN ISO 80000-2:2019

EN ISO 80000-2:2019 (E)

Contents Page

European foreword ....................................................................................................................................................... 3

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EN ISO 80000-2:2019 (E)

European foreword

This document (EN ISO 80000-2:2019) has been prepared by Technical Committee ISO/TC 12

"Quantities and units" in collaboration with Technical Committee CEN/SS F02 “Units and symbols” the

secretariat of which is held by CCMC.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 April 2020, and conflicting national standards shall be

withdrawn at the latest by April 2020.Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. CEN shall not be held responsible for identifying any or all such patent rights.

This document supersedes EN ISO 80000-2:2013.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, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,

Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of

North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the

United Kingdom.Endorsement notice

The text of ISO 80000-2:2019 has been approved by CEN as EN ISO 80000-2:2019 without any

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SIST EN ISO 80000-2:2019

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SIST EN ISO 80000-2:2019

INTERNATIONAL ISO

STANDARD 80000-2

Second edition

2019-08

Quantities and units —

Part 2:

Mathematics

Grandeurs et unités —

Partie 2: Mathématiques

Reference number

ISO 80000-2:2019(E)

ISO 2019

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ISO 80000-2:2019(E)

COPYRIGHT PROTECTED DOCUMENT

© ISO 2019

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.ISO copyright office

CP 401 • Ch. de Blandonnet 8

CH-1214 Vernier, Geneva

Phone: +41 22 749 01 11

Fax: +41 22 749 09 47

Email: copyright@iso.org

Website: www.iso.org

Published in Switzerland

ii © ISO 2019 – All rights reserved

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Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction ..................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions .................................................................................................................................................................................... 1

4 Variables, functions and operators ................................................................................................................................................... 1

5 Mathematical logic ............................................................................................................................................................................................. 2

6 Sets ...................................................................................................................................................................................................................................... 3

7 Standard number sets and intervals................................................................................................................................................ 4

8 Miscellaneous symbols .................................................................................................................................................................................. 6

9 Elementary geometry ...................................................................................................................................................................................... 7

10 Operations ................................................................................................................................................................................................................... 8

11 Combinatorics ......................................................................................................................................................................................................10

12 Functions ...................................................................................................................................................................................................................11

13 Exponential and logarithmic functions .....................................................................................................................................15

14 Circular and hyperbolic functions ...................................................................................................................................................16

15 Complex numbers.............................................................................................................................................................................................18

16 Matrices ......................................................................................................................................................................................................................18

17 Coordinate systems .........................................................................................................................................................................................19

18 Scalars, vectors and tensors ..................................................................................................................................................................21

19 Transforms ..............................................................................................................................................................................................................25

20 Special functions ................................................................................................................................................................................................26

Bibliography .............................................................................................................................................................................................................................32

Alphabetical index .............................................................................................................................................................................................................33

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ISO 80000-2:2019(E)

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.The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/directives).

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. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/patents).Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www .iso

.org/iso/foreword .html.This document was prepared by Technical Committee ISO/TC 12, Quantities and units, in collaboration

with Technical Committee IEC/TC 25, Quantities and units.This second edition cancels and replaces the first edition (ISO 80000-2:2009), which has been

technically revised.The main changes compared to the previous edition are as follows:

— Clause 4 revised to add clarification about writing of font types; revised rule for splitting equations

over two or more lines;— Clause 18 revised to include clarification on scalars, vectors and tensors;

— missing symbols and expressions added in the second column "Symbol, expression" of the tables,

and additional clarifications given in the fourth column “Remarks and examples” when necessary;

— Annex A deleted.NOTE Although missing symbols and expressions have been added in this second edition of ISO 80000-1, the

document remains non exhaustive.A list of all parts in the ISO 80000 and IEC 80000 series can be found on the ISO and IEC websites.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www .iso .org/members .html.iv © ISO 2019 – All rights reserved

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Introduction

Arrangement of the tables

Each table of symbols and expressions (except Table 13) gives hints (in the third column) about the

meaning or how the expression may be read for each item (numbered in the first column) of the

symbol under consideration, usually in the context of a typical expression (second column). If more

than one 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 purpose of the entries is

identification of each concept and is not intended to be a complete mathematical definition. The fourth

column “Remarks and examples” gives further information and is not normative.Table 13 has a different format. It gives the symbols of coordinates, as well as the position vectors and

their differentials, for coordinate systems in three-dimensional spaces.© ISO 2019 – All rights reserved v

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INTERNATIONAL STANDARD ISO 80000-2:2019(E)

Quantities and units —

Part 2:

Mathematics

1 Scope

This document specifies mathematical symbols, explains their meanings, and gives verbal equivalents

and applications.This document is intended mainly for use in the natural sciences and technology, but also applies to

other areas where mathematics is used.2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements 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, Quantities and units — Part 1: General3 Terms and definitions

Tables 1 to 16 give the symbols and expressions used in the different fields of mathematics.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https: //www .iso .org/obp— IEC Electropedia: available at http: //www .electropedia .org/

4 Variables, functions and operators

It is customary to use different sorts of letters for different sorts of entities, e.g. x, y, … for numbers

or elements of some given set, f, g for functions, etc. This makes formulas more readable and helps in

setting up an appropriate context.Variables such as x, y, etc., and running numbers, such as i in x are printed in italic type. Parameters,

such as a, b, etc., which may be considered as constant in a particular context, are printed in italic 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 upright type, e.g.

sin, exp, ln, Γ. Mathematical constants, the values of which never change, are printed in upright type,

e.g. e = 2,718 281 828 …; π = 3,141 592 …; i = −1. Well-defined operators are also printed in upright

type, e.g. div, δ in δx and each d in df/dx. Some transforms use special capital letters (see Clause 19,

Transforms).Numbers expressed in the form of digits are always printed in upright type, e.g. 351 204; 1,32; 7/8.

Binary operators, for example +, −, /, shall be preceded and followed by thin spaces. This rule does not

apply in case of unary operators, as in −17,3.© ISO 2019 – All rights reserved 1

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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(ω t + φ). 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 shall be a thin space

between the symbol for the function and the argument, e.g. int 2,4; sin nπ; 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).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, the following method shall be used:

— Place the line breaks immediately before one of the symbols =, +, −, ±, or , or, if necessary,

immediately before one of the symbols ×, ⋅, or /.The symbol shall not be given twice around the line break; two minus signs could for example give rise

to sign errors. If possible, the line break should not be inside of an expression in parentheses.

5 Mathematical logicTable 1 — Symbols and expressions in mathematical logic

Symbol,

Item No. Meaning, verbal equivalent Remarks and examples

expression

2-5.1 p ∧ q conjunction of p and q,

p and q

2-5.2 p ∨ q disjunction of p and q, This “or” is inclusive, i.e. p ∨ q is true, if

either p or q, or both are true.p or q

2-5.3 ¬ p negation of p,

not p

2-5.4 p ⇒ q p implies q, q ⇐ p has the same meaning as p ⇒ q.

if p, then q ⇒ is the implication symbol.

→ is also used as implication symbol.

2-5.5 p ⇔ q p is equivalent to q (p ⇒ q) ∧ (q ⇒ p) has the same meaning as

p ⇔ q.

⇔ is the equivalence symbol.

↔ is also used as equivalence symbol.

2-5.6 ∀x ∈ A p(x) for every x belonging to A, the If it is clear from the context which set A is

proposition p(x) is true considered, the notation ∀x p(x) can be used.∀ is the universal quantifier.

For x ∈ A, see 2-6.1.

2-5.7 ∃x ∈ A p(x) there exists an x belonging to A for If it is clear from the context which set A is

which p(x) is true considered, the notation ∃x p(x) can be used.∃ is the existential quantifier.

For x ∈ A, see 2-6.1.

∃ x p(x) is used to indicate that there is ex-

actly one element for which p(x) is true.

∃! is also used for ∃ .

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6 Sets

Table 2 — Symbols and expressions for sets

Symbol,

Item No. Meaning, verbal equivalent Remarks and examples

expression

2-6.1 x ∈ A x belongs to A, A ∋ x has the same meaning as x ∈ A.

x is an element of the set A

2-6.2 y ∉ A y does not belong to A, A ∌ y has the same meaning as y ∉ A.

y is not an element of the set A The negating stroke may also be vertical.

2-6.3 {x , x , …, x } set with elements x , x , …, x Also {x | i ∈ I}, where I denotes a set of sub-

1 2 n 1 2 n iscripts.

2-6.4 {x ∈ A | p(x)} set of those elements of A for EXAMPLE

which the proposition p(x) is true

{x ∈ R | x ≥ 5}

If it is clear from the context which set A is

considered, the notation {x | p(x)} can be

used (for example {x | x ≥ 5}, if it is clear that

real numbers are considered).

Instead of the vertical line often a colon is

used as separator:

{x ∈ A : p(x)}.

2-6.5 card A number of elements in A, The cardinality can be a transfinite number.

cardinality of A The symbol ∣∣ is also used for absolute valueof a real number (see 2-10.16), modulus of a

complex number (see 2-15.4) and magnitude

of a vector (see 2-18.4).

2-6.6 the empty set

2-6.7 B ⊆ A B is included in A, Every element of B belongs to A.

B is a subset of A ⊂ is also used, but see remark to 2-6.8.

A ⊇ B has the same meaning as B ⊆ A.

2-6.8 B ⊂ A B is properly included in A, Every element of B belongs to A, but at least

one element of A does not belong to B.B is a proper subset of A

If ⊂ is used for 2-6.7, then ⊊ shall be used

for 2-6.8.

A ⊃ B has the same meaning as B ⊂ A.

2-6.9 A ∪ B union of A and B The set of elements which belong to at least

one of the sets A and B.

A ∪ B = {x | x ∈ A ∨ x ∈ B}

2-6.10 A ∩ B intersection of A and B The set of elements which belong to both

sets A and B.

A ∩ B = {x | x ∈ A ∧ x ∈ B}

2-6.11 union of the sets A , A , …, A The set of elements belonging to at least one

1 2 nof the sets A , A , ..., A

1 2 n

i=1 n

A = A ∪ … ∪ A

1 n

i

, and are also used,

i=1 iI∈

i=1

iI∈

where I denotes a set of subscripts.

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Table 2 (continued)

Symbol,

Item No. Meaning, verbal equivalent Remarks and examples

expression

2-6.12 intersection of the sets The set of elements belonging to all sets A ,

A , ..., A

2 n

A , A ,…, A

1 2 n

i

i=1

, and are also used,

i=1 iI∈

A = A ∩ … ∩ A

1 n iI∈

i

i=1

where I denotes a set of subscripts.

2-6.13 A ∖ B difference of A and B, The set of elements which belong to A but

not to B.

A minus B

A ∖ B = {x | x ∈ A ∧ x ∉ B}

The notation A − B should not be used.

CB is also used. CB is mainly used when

A A

B is a subset of A, and the symbol A may be

omitted if it is clear from the context which

set A is considered.

2-6.14 (a, b) ordered pair a, b, (a, b) = (c, d) if and only if a = c and b = d.

couple a, b If the comma can be mistaken as the deci-

mal sign, then the semicolon (;) or a stroke

(|) may be used as separator.

2-6.15 (a , a , …, a ) ordered n-tuple See remark to 2-6.14.

1 2 n

2-6.16 A × B Cartesian product of the sets A The set of ordered pairs (a, b) such that a ∈ A

and B and b ∈ B.A × B = {(x, y) | x ∈ A ∧ y ∈ B}

2-6.17 Cartesian product of the sets The set of ordered n-tuples (x , x , …, x )

1 2 n

such that x ∈ A , x ∈ A , …, x ∈ A .

1 1 2 2 n n

A , A , …, A

1 2 n

∏ i

AA××...×A is denoted by A , where n is the

i=1

number of factors in the product.

AA=×…×A

∏ in1

i=1

2-6.18 id identity relation on set A, id is the set of all pairs (x, x) where x ∈ A.

A AIf the set A is clear from the context, the

diagonal of A × A

subscript A can be omitted.

7 Standard number sets and intervals

Table 3 — Symbols and expressions for standard number sets and intervals

Symbol,

Item No. Meaning, verbal equivalent Remarks and examples

expression

2-7.1 the set of natural numbers,

N N = {0, 1, 2, 3, …}

the set of positive integers and zero

N = {1, 2, 3, …}

Other restrictions can be indicated in an

obvious way, as shown below.

N = {n ∈ N | n > 5}

> 5

The symbols IN and are also used.

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Table 3 (continued)

Symbol,

Item No. Meaning, verbal equivalent Remarks and examples

expression

2-7.2 the set of integers

Z Z = {…, −2, −1, 0, 1, 2, …}

Z = {n ∈ Z | n ≠ 0}

Other restrictions can be indicated in an

obvious way, as shown below.

Z = {n ∈ Z | n > −3}

> −3

The symbol is also used.

2-7.3 the set of rational numbers

Q = {r ∈ Q | r ≠ 0}

Other restrictions can be indicated in an

obvious way, as shown below.

Q = {r ∈ Q | r < 0}

< 0

The symbols QI and ℚ are also used.

2-7.4 the set of real numbers

R = {x ∈ R | x ≠ 0}

Other restrictions can be indicated in an

obvious way, as shown below.

R = {x ∈ R | x > 0}

> 0

The symbols IR and are also used.

2-7.5 the set of complex numbers

C *

C = {z ∈ C | z ≠ 0}

The symbol is also used.

2-7.6 the set of prime numbers

P P = {2, 3, 5, 7, 11, 13, 17, …}

The symbol ℙ is also used.

2-7.7 [a, b] closed interval from a included

[a, b] = {x ∈ R | a ≤ x ≤ b}

to b included

2-7.8 (a, b] left half-open interval from a

(a, b] = {x ∈ R | a < x ≤ b}

excluded to b included

The notation ]a, b] is also used.

2-7.9 [a, b) right half-open interval from a

[a, b) = {x ∈ R | a ≤ x < b}

included to b excluded

The notation [a, b[ is also used.

2-7.10 (a, b) open interval from a excluded to b

(a, b) = {x ∈ R | a < x < b}

excluded

The notation ]a, b[ is also used.

2-7.11 (−∞, b] closed unbounded interval up to b

(−∞, b] = {x ∈ R | x ≤ b}

included

The notation ]−∞, b] is also used.

2-7.12 (−∞, b) open unbounded interval up to b

(−∞, b) = {x ∈ R | x < b}

excluded

The notation ]−∞, b[ is also used.

2-7.13 [a, +∞) closed unbounded interval on-

[a, +∞) = {x ∈ R | a ≤ x}

ward from a included

The notations [a, ∞), [a, +∞[ and [a, ∞[ are

also used.

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Table 3 (continued)

Symbol,

Item No. Meaning, verbal equivalent Remarks and examples

expression

2-7.14 (a, +∞) open unbounded interval onward

(a, +∞) = {x ∈ R | a < x}

from a excluded

The notations (a, ∞), ]a, +∞[ and ]a, ∞[ are

also used.

8 Miscellaneous symbols

Table 4 — Miscellaneous symbols and expressions

Symbol,

Item No. Meaning, verbal equivalent Remarks and examples

expression

2-8.1 a = b a is equal to b The symbol ≡ may be used to emphasize

that a particular equality is an identity, i.e.

a equals b

holds universally.

But see 2-8.18 for another meaning.

2-8.2 a ≠ b a is not equal to b The negating stroke may also be vertical.

2-8.3 a ≔ b a is by definition equal to b EXAMPLE

p ≔ mv , where p is momentum, m is mass

and v is velocity.

The symbols = and ≝ are also used.

def

2-8.4 a ≙ b a corresponds to b EXAMPLES

When E = kT, then 1 eV ≙ 11 604,5 K.

When 1 cm on a map corresponds

to a length of 10 km, one may write

1 cm ≙ 10 km.

The correspondence is not symmetric.

2-8.5 a ≈ b a is approximately equal to b It depends on the user whether an approx-

imation is sufficiently good. Equality is notexcluded.

2-8.6 a ≃ b a is asymptotically equal to b EXAMPLE

1 1

≃ as x → a

sin xa− xa−

(For x → a, see 2-8.16.)

2-8.7 a ~ b a is proportional to b The symbol ~ is also used for equivalence

relations.

The notation a ∝ b is also used.

2-8.8 M ≅ N M is congruent to N, M and N are point sets (geometrical figures).

M is isomorphic to N This symbol is also used for isomorphisms

of mathematical structures.

2-8.9 a < b a is less than b

2-8.10 b > a b is greater than a

2-8.11 a ≤ b a is less than or equal to b

2-8.12 b ≥ a b is greater than or equal to a

2-8.13 a ≪ b a is much less than b It depends on the situation whether a is

sufficiently small as compared to b.

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Table 4 (continued)

Symbol,

Item No. Meaning, verbal equivalent Remarks and examples

expression

2-8.14 b ≫ a b is much greater than a It depends on the situation whether b is

sufficiently great as compared to a.

2-8.15 ∞ infinity This symbol does not denote a number but

is often part of various expressions dealing

with limits.

The notations +∞, −∞ are also used.

2-8.16 x → a x tends to a This symbol occurs as part of various ex-

pressions dealing with limits.

a may be also ∞, +∞, or −∞.

2-8.17 m ∣ n m divides n For integers m and n:

∃ k ∈ Z m⋅k = n

2-8.18 n ≡ k mod m n is congruent to k modulo m For integers n, k and m:

m ∣ (n − k)

This concept of number theory must not be

confused with identity of an equation, men-

tioned in 2-8.1, column 4.

2-8.19 (a + b) parentheses It is recommended to use only parentheses

for grouping, since brackets and braces

[a + b] square brackets

often have a specific meaning in particular

{a + b} braces fields. Parentheses can be nested without

ambiguity.

〈a + b〉 angle brackets

9 Elementary geometry

Table 5 — Symbols and expressions in elementary geometry

Symbol,

Item No. Meaning, verbal equivalent Remarks and examples

expression

2-9.1 AB∥CD the straight line AB is parallel to It is written g ∥ h if g and h are the straight

the straight line CD lines determined by the points A and B, andthe points C and D, respectively.

2-9.2 AB⊥CD the

**...**

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