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 second line contains an informal definition, and the third line gives a short example.
Note: If some of the symbols don't display properly for you, then your browser does not completely implement the HTML 4 character entities, or you have to install additional fonts. You can check your browser here.
Symbol  Name  reads as  Category 

addition  plus  arithmetic  
4 + 6 = 10 means that if four is added to 6, the sum, or result, is 10.  
43 + 65 = 108; 2 + 7 = 9
 
subtraction  minus  arithmetic  
9  4 = 5 means that if 4 is subtracted from 9, the result will be 5. The  sign is unique in that it can also denote that a number is negative. For example, 5 + (3) = 2 means that if five and negative three are added, the result is two.  
87  36 = 51
 
material implication  implies; if .. then  propositional logic  
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 mentioned further down  
x = 2 ⇒ x^{2} = 4 is true, but x^{2} = 4 ⇒ x = 2 is in general false (since x could be −2)
 
material equivalence  if and only if; iff  propositional logic  
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
 
logical conjunction  and  propositional logic  
the statement A ∧ B 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
 
logical disjunction  or  propositional logic  
the statement A ∨ B 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
 
logical negation  not  propositional logic  
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 ∧ B) ⇔ (¬A) ∨ (¬B); x ∉ S ⇔ ¬(x ∈ S)
 
universal quantification  for all; for any; for each  predicate logic  
∀ x: P(x) means: P(x) is true for all x  
∀ n ∈ N: n^{2} ≥ n  
existential quantification  there exists  predicate logic  
∃ x: P(x) means: there is at least one x such that P(x) is true  
∃ n ∈ N: n + 5 = 2n
 
equality  equals  everywhere  
x = y means: x and y are different names for precisely the same thing  
1 + 2 = 6 − 3
 
definition  is defined as  everywhere  
x := y means: x is defined to be another name for y 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)
 
set brackets  the set of ...  set theory  
{a,b,c} means: the set consisting of a, b, and c  
N = {0,1,2,...}
 
set builder notation  the set of ... such that ...  set theory  
{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 : n^{2} < 20} = {0,1,2,3,4}
 
empty set  empty set  set theory  
{} means: the set with no elements; ∅ is the same thing  
{n ∈ N : 1 < n^{2} < 4} = {}  
set membership  in; is in; is an element of; is a member of; belongs to  set theory  
a ∈ S means: a is an element of the set S; a ∉ S means: a is not an element of S  
(1/2)^{−1} ∈ N; 2^{−1} ∉ N
 
subset  is a subset of  set theory  
A ⊆ B means: every element of A is also element of B A ⊂ B means: A ⊆ B but A ≠ B  
A ∩ B ⊆ A; Q ⊂ R
 
set theoretic union  the union of ... and ...; union  set theory  
A ∪ B means: the set that contains all the elements from A and also all those from B, but no others  
A ⊆ B ⇔ A ∪ B = B
 
set theoretic intersection  intersected with; intersect  set theory  
A ∩ B means: the set that contains all those elements that A and B have in common  
{x ∈ R : x^{2} = 1} ∩ N = {1}
 
set theoretic complement  minus; without  set theory  
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}
 
function application; grouping  of  set theory  
for function application: f(x) means: the value of the function f at the element x for grouping: perform the operations inside the parentheses first  
If f(x) := x^{2}, then f(3) = 3^{2} = 9; (8/4)/2 = 2/2 = 1, but 8/(4/2) = 8/2 = 4
 
function arrow  from ... to  functions  
f: X → Y means: the function f maps the set X into the set Y  
Consider the function f: Z → N defined by f(x) = x^{2}
 
natural numbers  N  numbers  
N means: {0,1,2,3,...}  
{a : a ∈ Z} = N
 
integers  Z  numbers  
Z means: {...,−3,−2,−1,0,1,2,3,...}  
{a : a ∈ N} = Z
 
rational numbers  Q  numbers  
Q means: {p/q : p,q ∈ Z, q ≠ 0}  
3.14 ∈ Q; π ∉ Q
 
real numbers  R  numbers  
R means: {lim_{n→∞} a_{n} : ∀ n ∈ N: a_{n} ∈ Q, the limit exists}  
π ∈ R; √(−1) ∉ R
 
C  complex numbers  C  numbers 
C means: {a + bi : a,b ∈ R}  
i = √(−1) ∈ C
 
comparison  is less than, is greater than  partial orders  
x < y means: x is less than y; x > y means: x is greater than y  
x < y ⇔ y > x
 
comparison  is less than or equal to, is greater than or equal to  partial orders  
x ≤ y means: x is less than or equal to y; x ≥ y means: x is greater than or equal to y  
x ≥ 1 ⇒ x^{2} ≥ x
 
square root  the principal square root of; square root  real numbers  
√x means: the positive number whose square is x  
√(x^{2}) = x
 
infinity  infinity  numbers  
∞ is an element of the extended number line that is greater than all real numbers; it often occurs in limits  
lim_{x→0} 1/x = ∞
 
pi  pi  Euclidean geometry  
π means: the ratio of a circle's circumference to its diameter  
A = πr² is the area of a circle with radius r
 
factorial  factorial  combinatorics  
n! is the product 1×2×...×n  
4! = 12
 
absolute value  absolute value of  numbers  
x means: the distance in the real line (or the complex plane) between x and zero  
a + bi = √(a^{2} + b^{2})
 
norm  norm of; length of  functional analysis  
x is the norm of the element x of a normed vector space  
x+y ≤ x + y
 
summation  sum over ... from ... to ... of  arithmetic  
∑_{k=1}^{n} a_{k} means: a_{1} + a_{2} + ... + a_{n}  
∑_{k=1}^{4} k^{2} = 1^{2} + 2^{2} + 3^{2} + 4^{2} = 1 + 4 + 9 + 16 = 30
 
product  product over ... from ... to ... of  arithmetic  
∏_{k=1}^{n} a_{k} means: a_{1}a_{2}···a_{n}  
∏_{k=1}^{4} (k + 2) = (1 + 2)(2 + 2)(3 + 2)(4 + 2) = 3 × 4 × 5 × 6 = 360
 
integration  integral from ... to ... of ... with respect to  calculus  
∫_{a}^{b} f(x) dx means: the signed area between the xaxis and the graph of the function f between x = a and x = b  
∫_{0}^{b} x^{2} dx = b^{3}/3; ∫x^{2} dx = x^{3}/3
 
derivative  derivative of f; f prime  calculus  
f '(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 f '(x) = 2x
 
gradient  del, nabla, gradient of  calculus  
∇f (x_{1}, …, x_{n}) is the vector of partial derivatives (df / dx_{1}, …, df / dx_{n})  
If f (x,y,z) = 3xy + z² then ∇f = (3y, 3x, 2z) A transparent image for text is: Image:Del.gif ().  
insert more  

If some of these symbols are used in a Wikipedia article that is intended for beginners, it may be a good idea to include a statement like the following below the definition of the subject in order to reach a broader audience:
 ''This article uses [[table of mathematical symbolsmathematical symbols]].''
External links:
 Jeff Miller: ''Earliest Uses of Various Mathematical Symbols, http://members.aol.com/jeff570/mathsym.html
 TCAEP  Institute of Physics, http://www.tcaep.co.uk/science/symbols/maths.htm