# GetWiki:Symbols Table

ARTICLE SUBJECTS

being →

database →

ethics →

fiction →

history →

internet →

language →

linux →

logic →

method →

news →

policy →

purpose →

religion →

science →

software →

truth →

unix →

wiki →

ARTICLE TYPES

essay →

feed →

help →

system →

wiki →

ARTICLE ORIGINS

critical →

forked →

imported →

original →

index
GetWiki:Symbols Table

GetWiki&Overview | 1.0/2.0/3.0/InterWiki | SOHOdb

Custom Messages/Links/Images/Formulas/Chars&Symbols

Custom Messages/Links/Images/Formulas/Chars&Symbols

In Mathematics, a set of symbols is frequently used in mathematical expressions. As mathematicians are familiar with these symbols, they are not explained each time they are used. So, for mathematical novices, the following table lists many common symbols together with their name, pronunciation and related field of Mathematics. Additionally, the third column contains an informal definition, and the fourth column gives a short example.

Be aware that, in some cases, different symbols have the same meaning, and the same symbol has, depending on the context, different meanings.

*Note: The large table below has a mysterious origin, but it has often served as a complex testbed for GetWiki’s new table rendering code.*

## Basic Mathematical Symbols

Symbol |
Name |
Explanation |
Example |
||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Read As |
|||||||||||||

Category |
|||||||||||||

= |
equality | xÂ = y means x and y represent the same thing or value. |
1Â + 1Â = 2 | ||||||||||

is equal to; equals | |||||||||||||

everywhere | |||||||||||||

? |
Inequation | x ? y means that x and y do not represent the same thing or value. |
1 ? 2 | ||||||||||

is not equal to; does not equal | |||||||||||||

everywhere | |||||||||||||

+ |
addition | 4 + 6 means the sum of 4 and 6. | 2 + 7 = 9 | ||||||||||

plus | |||||||||||||

arithmetic | |||||||||||||

? |
subtraction | 9 ? 4 means the subtraction of 4 from 9. | 8 ? 3 = 5 | ||||||||||

minus | |||||||||||||

arithmetic | |||||||||||||

negative_sign | ?3 means the negative of the number 3. | ?(?5) = 5 | |||||||||||

negative | |||||||||||||

arithmetic | |||||||||||||

set theoretic complement | AÂ ?Â B means the set that contains all the elements of A that are not in B |
{1,2,3,4}Â ?Â {3,4,5,6}Â Â =Â Â {1,2} | |||||||||||

minus; without | |||||||||||||

set_theory | |||||||||||||

Ã— |
multiplication | 3 Ã— 4 means the multiplication of 3 by 4. | 7 Ã— 8 = 56 | ||||||||||

times | |||||||||||||

arithmetic | |||||||||||||

cartesian product | XÃ—Y means the set of all ordered pairs with the first element of each pair selected from X and the second element selected from Y. |
{1,2} Ã— {3,4} = {(1,3),(1,4),(2,3),(2,4)} | |||||||||||

the cartesian product of â€¦ and â€¦; the direct product of â€¦ and â€¦ | |||||||||||||

set_theory | |||||||||||||

Ã· / |
division | 6 Ã· 3 or 6/3 means the division of 6 by 3. | 2 Ã· 4 = .5 12/4 = 3 |
||||||||||

divided by | |||||||||||||

arithmetic | |||||||||||||

? ? ? |
material implication | A ? B means if A is true then B is also true; if A is false then nothing is said about B.? may mean the same as ?, or it may have the meaning for functions given below; ? may mean the same as ?, or it may have the meaning for superset given below; |
x = 2Â Â ?Â x^{2} = 4 is true, but x^{2} = 4 Â Â ?Â x = 2 is in general false (since x could be ?2) |
||||||||||

implies; if .. then | |||||||||||||

propositional_logic | |||||||||||||

? ? |
material equivalence | AÂ ? B means A is true if B is true and A is false if B is false |
xÂ + 5Â = yÂ +2Â Â ?Â xÂ + 3Â = y |
||||||||||

if and only if; iff | |||||||||||||

propositional_logic | |||||||||||||

Â¬ |
logical negation | the statement Â¬A is true if and only if A is falsea slash placed through another operator is the same as “Â¬” placed in front |
Â¬(Â¬A)Â ? A xÂ ?Â yÂ Â ?Â Â¬(xÂ =Â y) |
||||||||||

not | |||||||||||||

propositional_logic | |||||||||||||

? |
logical conjunction or meet in a lattice |
the statement A ? B is true if A and B are both true; else it is false |
nÂ < 4Â Â ?Â nÂ >2Â Â ?Â nÂ = 3 when n is a natural number |
||||||||||

and | |||||||||||||

propositional_logic, lattice_theory | |||||||||||||

? |
logical disjunction or join in a lattice |
the statement A ? B is true if A or B (or both) are true; if both are false, the statement is false |
nÂ ? 4Â Â ?Â nÂ ? 2Â Â ? nÂ ? 3 when n is a natural number |
||||||||||

or | |||||||||||||

propositional_logic, lattice_theory | |||||||||||||

? ? |
exclusive or | A &o(lus; B is true when either A or B are true, but not when both are true |
(Â¬A) &o(lus; A is always true, A &o(lus; A is always false |
||||||||||

xor | |||||||||||||

propositional_logic, boolean algebra | |||||||||||||

? |
universal quantification | ?Â x: P(x) means P(x) is true for all x |
?Â nÂ ? N: n^{2}Â ? n |
||||||||||

for all; for any; for each | |||||||||||||

predicate logic | |||||||||||||

? |
existential quantification | ?Â x: P(x) means there is at least one x such that P(x) is true |
?Â nÂ ? N: nÂ + 5Â = 2n |
||||||||||

there exists | |||||||||||||

predicate logic | |||||||||||||

:= ? :? |
definition | xÂ := y or xÂ ? y means x is defined to be another name for y (but note that ? can also mean other things, such as congruence) PÂ :? Q means P is defined to be logically equivalent to Q |
coshÂ xÂ := (1/2)(expÂ xÂ + expÂ (?x)); A XOR BÂ :? (AÂ ? B)Â ? Â¬(AÂ ? B) |
||||||||||

is defined as | |||||||||||||

everywhere | |||||||||||||

{ , } |
set brackets | {a,b,c} means the set consisting of a, b, and c |
NÂ = {0,1,2,...} |
||||||||||

the set of ... | |||||||||||||

set_theory | |||||||||||||

{ : } { | } |
set_theory | {xÂ : P(x)} means the set of all x for which P(x) is true. {xÂ | P(x)} is the same as {xÂ : P(x)}. |
{nÂ ? NÂ : n^{2}Â <Â 20}Â = {0,1,2,3,4} |
||||||||||

the set of ... such that ... | |||||||||||||

naive set | |||||||||||||

? {} |
empty set | {} means the set with no elements; ? is the same thing | {nÂ ? NÂ : 1Â < n^{2}Â < 4}Â = {} |
||||||||||

empty set | |||||||||||||

set_theory | |||||||||||||

? ? |
set membership | aÂ ? S means a is an element of the set S; aÂ ? S means a is not an element of S |
(1/2)^{?1}Â ? N; 2^{?1}Â ? N |
||||||||||

is an element of; is not an element of | |||||||||||||

everywhere, set_theory | |||||||||||||

? ? |
subset | AÂ ? B means every element of A is also element of BAÂ ? B means AÂ ? B but AÂ ? B |
AÂ ? B ? A; QÂ ? R |
||||||||||

is a subset of | |||||||||||||

set_theory | |||||||||||||

? ? |
superset | AÂ ? B means every element of B is also element of AAÂ ? B means AÂ ? B but AÂ ? B |
AÂ ? B ? B; RÂ ? Q |
||||||||||

is a superset of | |||||||||||||

set_theory | |||||||||||||

? |
set theoretic union | AÂ ? B means the set that contains all the elements from A and also all those from B, but no others |
AÂ ? BÂ Â ?Â AÂ ? BÂ = B |
||||||||||

the union of ... and ...; union | |||||||||||||

set_theory | |||||||||||||

? |
set theoretic intersection | AÂ ? B means the set that contains all those elements that A and B have in common |
{xÂ ? RÂ : x^{2}Â = 1}Â ? NÂ = {1} |
||||||||||

intersected with; intersect | |||||||||||||

set_theory | |||||||||||||

set theoretic complement | AÂ B means the set that contains all those elements of A that are not in B |
{1,2,3,4} {3,4,5,6} = {1,2} | |||||||||||

minus; without | |||||||||||||

set_theory | |||||||||||||

( ) |
function application | f(x) means the value of the function f at the element x |
If f(x)Â := x^{2}, then f(3)Â = 3^{2}Â = 9 |
||||||||||

of | |||||||||||||

set_theory | |||||||||||||

precedence grouping | perform the operations inside the parentheses first | (8/4)/2Â = 2/2Â = 1, but 8/(4/2)Â = 8/2Â = 4 | |||||||||||

everywhere | |||||||||||||

f:X?Y |
function arrow | f:Â XÂ ? Y means the function f maps the set X into the set Y |
Consider the function f:Â ZÂ ? N defined by f(x)Â = x^{2} |
||||||||||

from ... to | |||||||||||||

functions | |||||||||||||

N ? |
natural numbers | N means {0,1,2,3,...}, but see the article on natural numbers for a different convention. |
{ | a>Â : aÂ ? Z}Â = N |
|||||||||

N | |||||||||||||

numbers | |||||||||||||

Z ? |
integers | Z means {...,?3,?2,?1,0,1,2,3,...} |
{aÂ : |
a>Â ? N}Â = Z |
|||||||||

Z | |||||||||||||

numbers | |||||||||||||

Q ? |
rational numbers | Q means {p/qÂ : p,qÂ ? Z, qÂ ? 0} |
3.14Â ? Q; ?Â ? Q |
||||||||||

Q | |||||||||||||

numbers | |||||||||||||

R ? |
real numbers | R means {lim_{n??}Â a_{n}Â : ?Â nÂ ? N: a_{n}Â ? Q, the limit exists} |
?Â ? R; ?(?1)Â ? R |
||||||||||

R | |||||||||||||

numbers | |||||||||||||

C ? |
complex numbers | C means {aÂ + biÂ : a,bÂ ? R} |
iÂ = ?(?1)Â ? C |
||||||||||

C | |||||||||||||

numbers | |||||||||||||

< > |
strict_inequality | xÂ < y means x is less than y; xÂ > y means x is greater than y |
xÂ < yÂ Â ?Â yÂ > x |
||||||||||

is less than, is greater than | |||||||||||||

partial orders | |||||||||||||

? ? |
inequality | xÂ ? y means x is less than or equal to y; xÂ ? y means x is greater than or equal to y |
xÂ ? 1Â Â ?Â x^{2}Â ? x |
||||||||||

is less than or equal to, is greater than or equal to | |||||||||||||

partial orders | |||||||||||||

? |
square root | ?x means the positive number whose square is x |
?(x^{2})Â = |
x> | |||||||||

the principal square root of; square root | |||||||||||||

real numbers | |||||||||||||

? |
infinity | ? is an element of the extended_number_line that is greater than all real numbers; it often occurs in limits | lim_{x?0}Â 1/ |
x>Â = ? | |||||||||

infinity | |||||||||||||

numbers | |||||||||||||

? |
pi | ? means the ratio of a circle’s circumference to its diameter | AÂ = ?rÂ² is the area of a circle with radius r |
||||||||||

pi | |||||||||||||

Euclidean geometry | |||||||||||||

! |
factorial | n! is the product 1Ã—2Ã—...Ã—n |
4! = 24 | ||||||||||

factorial | |||||||||||||

combinatorics | |||||||||||||

absolute value | x> means the distance in the real line (or the complex plane) between x and zero |
aÂ + bi>Â = ?(a^{2}Â + b^{2}) |
|||||||||||

absolute value of | |||||||||||||

numbers | |||||||||||||

Â | norm | x |
is the norm of the element x of a normed vector space |
x+y |
? | x |
+ | y |
|||||

norm of; length of | |||||||||||||

functional analysis | |||||||||||||

? |
summation | ?_{k=1}^{n}Â a_{k} means a_{1}Â + a_{2}Â + ...Â + a_{n} |
?_{k=1}^{4}Â k^{2}Â = 1^{2}Â + 2^{2}Â + 3^{2}Â + 4^{2}Â = 1Â + 4Â + 9Â + 16Â = 30 |
||||||||||

sum over ... from ... to ... of | |||||||||||||

arithmetic | |||||||||||||

? |
product | ?_{k=1}^{n}Â a_{k} means a_{1}a_{2}Â·Â·Â·a_{n} |
?_{k=1}^{4}Â (kÂ + 2)Â = (1Â + 2)(2Â + 2)(3Â + 2)(4Â + 2)Â = 3Â Ã— 4Â Ã— 5Â Ã— 6Â = 360 |
||||||||||

product over ... from ... to ... of | |||||||||||||

arithmetic | |||||||||||||

cartesian product | ?_{i=0}^{n}Y_{i} means the set of all (n+1)-tuples (y_{0},...,y_{n}). |
?_{n=1}^{3}R = R^{n} |
|||||||||||

the cartesian product of; the direct product of | |||||||||||||

set_theory | |||||||||||||

? |
integration | ?_{a}^{b}Â f(x)Â dx means the signed area between the x-axis and the graph of the function f between xÂ = a and xÂ = b |
?_{0}^{b}Â x^{2 }Â dxÂ = b^{3}/3; ?x^{2}Â dxÂ = x^{3}/3 |
||||||||||

integral from ... to ... of ... with respect to | |||||||||||||

calculus | |||||||||||||

fÂ ’ |
derivative | fÂ ’(x) is the derivative of the function f at the point x, i.e., the slope of the tangent there |
If f(x) = x^{2}, then fÂ ’(x) = 2x and fÂ (x’’) = 2 |
||||||||||

derivative of f; f prime | |||||||||||||

calculus | |||||||||||||

? |
gradient | ?f (x_{1}, â€¦, x_{n}) is the vector of partial derivatives (df / dx_{1}, â€¦, df / dx_{n}) |
If f (x,y,z) = 3xy + zÂ² then ?f = (3y, 3x, 2z) |
||||||||||

del, nabla, gradient of | |||||||||||||

calculus | |||||||||||||

? |
partial | With f (x_{1}, â€¦, x_{n}), ?f/?x_{i} is the derivative of f with respect to x_{i}, with all other variables kept constant. |
If f(x,y) = x^{2}y, then ?f/?x = 2xy |
||||||||||

partial derivative of | |||||||||||||

calculus | |||||||||||||

? |
perpendicular | x ? y means x is perpendicular to y; or more generally x is orthogonal to y. |
|||||||||||

is perpendicular to | |||||||||||||

orthogonality | |||||||||||||

bottom element | x = ? means x is the smallest element. |
||||||||||||

the bottom element | |||||||||||||

lattice_theory | |||||||||||||

? |
entailment | a means the sentence models ba entails the sentence b. Formal definition: a if and only if, in every model in which models ba is true, b is also true. |
|||||||||||

entails | |||||||||||||

propositional_logic, predicate logic | |||||||||||||

? |
inference | x vdash y means y is derived from x. |
|||||||||||

infers or is derived from | |||||||||||||

propositional_logic, predicate logic |

NOTE: If some of these symbols are used in an article intended for beginners, it may be a good idea to include a statement like the below, included with the {{msg:symbols}} code. This will help the article reach a broader audience:

*This article uses mathematical symbols.*

## External Links

- Official Code Chart
- Jeff Miller: ‘’Earliest Uses of Various Mathematical Symbols”
- TCAEP - Institute of Physics

GetWiki&Overview | 1.0/2.0/3.0/InterWiki | SOHOdb

Custom Messages/Links/Images/Formulas/Chars&Symbols

Custom Messages/Links/Images/Formulas/Chars&Symbols

*Some content adapted from the Wikinfo article “Table of mathematical symbols” under the GNU Free Documentation License.*

[ last updated: 4:48pm EDT - Sun, Jun 02 2024 ]

[

[

*getwiki edits: 5 , site views: 2,445*]LATEST EDITS [ see all ]

GETWIKI 17 JUN 2024

GETWIKI 11 JUN 2024

GETWIKI 10 JUN 2024

GETWIKI 02 JUN 2024

GETWIKI 01 JUN 2024

© 2007-2024, 2004-2024 M.R.M. PARROTT | ALL RIGHTS RESERVED