Wikia

Psychology Wiki

Table of mathematical symbols

Talk0
34,141pages on
this wiki
Revision as of 23:09, August 15, 2012 by Dr Joe Kiff (Talk | contribs)

Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Individual differences | Personality | Philosophy | Social |
Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology |

Statistics: Scientific method · Research methods · Experimental design · Undergraduate statistics courses · Statistical tests · Game theory · Decision theory


The following table lists many specialized symbols commonly used in mathematics. For the HTML codes of mathematical symbols see mathematical HTML.

Note: This article contains special characters.

Basic mathematical symbols

Symbol
Name Explanation Examples
Should be read as
Category
=
equality x = y means x and y represent the same thing or value. 1 + 1 = 2
is equal to; equals
everywhere


<>
inequation xy means that x and y do not represent the same thing or value. 1 ≠ 2
is not equal to; does not equal
everywhere
<

>



strict inequality x < y means x is less than y.

x > y means x is greater than y.

x ≪y means x is much less than y.

x ≫ y means x is much greater than y.
3 < 4
5 > 4.

0.003 ≪1,000,000

is less than, is greater than, is much less than, is much greater than
order theory


inequality x ≤ y means x is less than or equal to y.

x ≥ y means x is greater than or equal to y.
3 ≤ 4 and 5 ≤ 5
5 ≥ 4 and 5 ≥ 5
is less than or equal to, is greater than or equal to
order theory
proportionality yx means that y = kx for some constant k. if y = 2x, then yx
is proportional to
everywhere
+
addition 4 + 6 means the sum of 4 and 6. 2 + 7 = 9
plus
arithmetic
disjoint union A1 + A2 means the disjoint union of sets A1 and A2. A1={1,2,3,4} ∧ A2={2,4,5,7} ⇒
A1 + A2 = {(1,1), (2,1), (3,1), (4,1), (2,2), (4,2), (5,2), (7,2)}
the disjoint union of … and …
set theory
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 ; minus
arithmetic
set-theoretic complement A − B means the set that contains all the elements of A that are not in B. {1,2,4} − {1,3,4}  =  {2}
minus; without
set theory
×
multiplication 3 × 4 means the multiplication of 3 by 4. 7 × 8 = 56
times
arithmetic
Cartesian product X×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} × {3,4} = {(1,3),(1,4),(2,3),(2,4)}
the Cartesian product of … and …; the direct product of … and …
set theory
cross product u × v means the cross product of vectors u and v (1,2,5) × (3,4,−1) =
(−22, 16, − 2)
cross
vector algebra
÷

/
division 6 ÷ 3 or 6/3 means the division of 6 by 3. 2 ÷ 4 = .5

12/4 = 3
divided by
arithmetic
square root x means the positive number whose square is x. √4 = 2
the principal square root of; square root
real numbers
complex square root if z = r exp(iφ) is represented in polar coordinates with -π < φ ≤ π, then √z = √r exp(iφ/2). √(-1) = i
the complex square root of; square root
complex numbers
| |
absolute value |x| means the distance in the real line (or the complex plane) between x and zero. |3| = 3, |-5| = |5|
|i| = 1, |3+4i| = 5
absolute value of
numbers
!
factorial n! is the product 1×2×...×n. 4! = 1 × 2 × 3 × 4 = 24
factorial
combinatorics
~
probability distribution X ~ D, means the random variable X has the probability distribution D. X ~ N(0,1), the standard normal distribution
has distribution
statistics




material implication AB 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 = 2  ⇒  x2 = 4 is true, but x2 = 4   ⇒  x = 2 is in general false (since x could be −2).
implies; if .. then
propositional logic


material equivalence A ⇔ B means A is true if B is true and A is false if B is false. x + 5 = y +2  ⇔  x + 3 = y
if and only if; iff
propositional logic
¬

˜
logical negation The statement ¬A is true if and only if A is false.

A slash placed through another operator is the same as "¬" placed in front.
¬(¬A) ⇔ A
x ≠ y  ⇔  ¬(x =  y)
not
propositional logic
logical conjunction or meet in a lattice The statement AB is true if A and B are both true; else it is false. n < 4  ∧  n >2  ⇔  n = 3 when n is a natural number.
and
propositional logic, lattice theory
logical disjunction or join in a lattice The statement AB is true if A or B (or both) are true; if both are false, the statement is false. n ≥ 4  ∨  n ≤ 2  ⇔ n ≠ 3 when n is a natural number.
or
propositional logic, lattice theory



exclusive or The statement AB is true when either A or B, but not both, are true. AB means the same. A) ⊕ A is always true, AA is always false.
xor
propositional logic, Boolean algebra
universal quantification ∀ x: P(x) means P(x) is true for all x. ∀ n ∈ N: n2 ≥ n.
for all; for any; for each
predicate logic
existential quantification ∃ x: P(x) means there is at least one x such that P(x) is true. ∃ n ∈ N: n is even.
there exists
predicate logic
∃!
uniqueness quantification ∃! x: P(x) means there is exactly one x such that P(x) is true. ∃! n ∈ N: n + 5 = 2n.
there exists exactly one
predicate logic
:=



:⇔
definition x := y or x ≡ y means x is defined to be another name for y (but note that ≡ can also mean other things, such as congruence).

P :⇔ Q means P is defined to be logically equivalent to Q.
cosh x := (1/2)(exp x + exp (−x))

A XOR B :⇔ (A ∨ B) ∧ ¬(A ∧ B)
is defined as
everywhere
{ , }
set brackets {a,b,c} means the set consisting of a, b, and c. N = {0,1,2,...}
the set of ...
set theory
{ : }

{ | }
set builder notation {x : P(x)} means the set of all x for which P(x) is true. {x | P(x)} is the same as {x : P(x)}. {n ∈ N : n2 < 20} = {0,1,2,3,4}
the set of ... such that ...
set theory

empty set Template:0/ means the set with no elements. {} means the same. {n ∈ N : 1 < n2 < 4} = Template:0/
the empty set
set theory
set membership a ∈ S means a is an element of the set S; a Template:Notin S means a is not an element of S. (1/2)−1 ∈ N

2−1 Template:Notin N
is an element of; is not an element of
everywhere, set theory


subset (subset) A ⊆ B means every element of A is also element of B.

(proper subset) A ⊂ B means A ⊆ B but A ≠ B.
A ∩ BA; Q ⊂ R
is a subset of
set theory


superset A ⊇ B means every element of B is also element of A.

A ⊃ B means A ⊇ B but A ≠ B.
A ∪ BB; R ⊃ Q
is a superset of
set theory
set-theoretic union (exclusive) A ∪ B means the set that contains all the elements from A, or all the elements from B, but not both.
"A or B, but not both".

(inclusive) A ∪ B means the set that contains all the elements from A, or all the elements from B, or all the elements from both A and B.
"A or B or both".
A ⊆ B  ⇔  A ∪ B = B (inclusive)
the union of ... and ...; union
set theory
set-theoretic intersection A ∩ B means the set that contains all those elements that A and B have in common. {x ∈ R : x2 = 1} ∩ N = {1}
intersected with; intersect
set theory
\
set-theoretic complement A \ 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) := x2, then f(3) = 32 = 9.
of
set theory
precedence grouping Perform the operations inside the parentheses first. (8/4)/2 = 2/2 = 1, but 8/(4/2) = 8/2 = 4.
everywhere
f:XY
function arrow fX → Y means the function f maps the set X into the set Y. Let fZ → N be defined by f(x) := x2.
from ... to
set theory
o
function composition fog is the function, such that (fog)(x) = f(g(x)). if f(x) := 2x, and g(x) := x + 3, then (fog)(x) = 2(x + 3).
composed with
set theory

N

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

Z

integers Z means {...,−3,−2,−1,0,1,2,3,...}. {a : |a| ∈ N} = Z
Z
numbers

Q

rational numbers Q means {p/q : p,q ∈ Z, q ≠ 0}. 3.14 ∈ Q

π ∉ Q
Q
numbers

R

real numbers R means the set of real numbers. π ∈ R

√(−1) ∉ R
R
numbers

C

complex numbers C means {a + bi : a,b ∈ R}. i = √(−1) ∈ C
C
numbers
infinity ∞ is an element of the extended number line that is greater than all real numbers; it often occurs in limits. limx→0 1/|x| = ∞
infinity
numbers
\pi
pi π is the ratio of a circle's circumference to its diameter. Its value is 3.1415.... A = πr² is the area of a circle with radius r
pi
Euclidean geometry
|| ||
norm ||x|| is the norm of the element x of a normed vector space. ||x+y|| ≤ ||x|| + ||y||
norm of; length of
linear algebra
summation k=1n ak means a1 + a2 + ... + an. k=14 k2 = 12 + 22 + 32 + 42 = 1 + 4 + 9 + 16 = 30
sum over ... from ... to ... of
arithmetic
product k=1n ak means a1a2···an. k=14 (k + 2) = (1  + 2)(2 + 2)(3 + 2)(4 + 2) = 3 × 4 × 5 × 6 = 360
product over ... from ... to ... of
arithmetic
Cartesian product i=0nYi means the set of all (n+1)-tuples (y0,...,yn). n=13R = Rn
the Cartesian product of; the direct product of
set theory
'
derivative f '(x) is the derivative of the function f at the point x, i.e., the slope of the tangent to f at x. If f(x) := x2, then f '(x) = 2x
… prime; derivative of …
calculus
indefinite integral or antiderivative ∫ f(x) dx means a function whose derivative is f. x2 dx = x3/3 + C
indefinite integral of …; the antiderivative of …
calculus
definite integral ab f(x) dx means the signed area between the x-axis and the graph of the function f between x = a and x = b. 0b x2  dx = b3/3;
integral from ... to ... of ... with respect to
calculus
gradient f (x1, …, xn) is the vector of partial derivatives (df / dx1, …, df / dxn). If f (x,y,z) := 3xy + z², then ∇f = (3y, 3x, 2z)
del, nabla, gradient of
calculus
partial derivative With f (x1, …, xn), ∂f/∂xi is the derivative of f with respect to xi, with all other variables kept constant. If f(x,y) := x2y, then ∂f/∂x = 2xy
partial derivative of
calculus
boundary M means the boundary of M ∂{x : ||x|| ≤ 2} = {x : ||x|| = 2}
boundary of
topology
perpendicular xy means x is perpendicular to y; or more generally x is orthogonal to y. If lm and mn then l || n.
is perpendicular to
geometry
bottom element x = ⊥ means x is the smallest element. x : x ∧ ⊥ = ⊥
the bottom element
lattice theory
entailment AB means the sentence A entails the sentence B, that is every model in which A is true, B is also true. AA ∨ ¬A
entails
model theory
inference xy means y is derived from x. AB ⊢ ¬B → ¬A
infers or is derived from
propositional logic, predicate logic
normal subgroup NG means that N is a normal subgroup of group G. Z(G) ◅ G
is a normal subgroup of
group theory
/
quotient group G/H means the quotient of group G modulo its subgroup H. {0, a, 2a, b, b+a, b+2a} / {0, b} = {{0, b}, {a, b+a}, {2a, b+2a}}
mod
group theory
isomorphism GH means that group G is isomorphic to group H Q / {1, −1} ≈ V,
where Q is the quaternion group and V is the Klein four-group.
is isomorphic to
group theory
approximately equal xy means x is approximately equal to y π ≈ 3.14159
is approximately equal to
everywhere


tensor product VU means the tensor product of V and U. {1, 2, 3, 4} ⊗ {1,1,2} =
{{1, 2, 3, 4}, {1, 2, 3, 4}, {2, 4, 6, 8}}
tensor product of
linear algebra

See also

External links

Special characters

Technical note: Due to technical limitations, many computers cannot display some of the special characters in this article. Such characters may be rendered as boxes, question marks, or other nonsense symbols, depending on your browser, operating system, and installed fonts. Even if you have ensured that your browser is interpreting the article as UTF-8 encoded and you have installed a font that supports a wide range of Unicode, such as Code2000, Arial Unicode MS, Lucida Sans Unicode or one of the free Unicode fonts, you may still need to use a different browser, as browser capabilities in this regard tend to vary.de:Wikipedia:Tabelle mathematischer Symbole es:Tabla de símbolos matemáticos fr:Table des symboles mathématiques id:Daftar simbol matematika nl:Lijst van wiskundige symbolenpt:Tabela de símbolos matemáticos ru:Таблица математических символов su:Tabel lambang matematis sv:Tabell över matematiska symboler zh:数学符号表

This page uses Creative Commons Licensed content from Wikipedia (view authors).

Around Wikia's network

Random Wiki