List of mathematical symbols

The list below has some of the most common symbols in mathematics. However, these symbols can have other meanings in different contexts other than math.^[source?]

Symbol	Name	Read as	Meaning	Example(s)
=	Equal	is equal to	If x=y, x and y represent the same value or thing.	5(2)=10
≡	Definition	is defined as	If x≡y, x is defined as another name of y	ϕ≡(√5+1)/2≈1.618
≈	Approximately equal	is approximately equal to	If x≈y, x and y are almost equal.	√2≈1.41
≠	Inequation	does not equal, is not equal to	If x≠y, x and y do not represent the same value or thing.	1+1≠3
<	Strict inequality	is strictly less than	If x<y, x is less than y.	4<5
>		is strictly greater than	If x>y, x is greater than y.	3>2
≪		is much less than	If x≪y, x is much less than y.	0.001≪999999999
≫		is much greater than	If x≫y, x is much greater than y.	999999999≫0.001
≤	Inequality	is less than	If x≤y, x is less than or equal to y.	5≤6 and 5≤5
≥		is greater than	If x≥y, x is greater than or equal to y.	2≥1 and 2≥2
∝	Proportionality	is proportional to	If x∝y, then y=kx for some constant k.	If y=4x then y∝x and x∝y
+	Addition	plus	x+y is the sum of x and y.	2+3=5
-	Subtraction	minus	x-y is the subtraction of y from x	5-3=2
× or · or *	Multiplication	times or multiplied by	x×y or x·y is the multiplication of x by y	4×5=20 or 4·5=20
÷ or / or :	Division	divided by	x÷y or x/y is the division of x by y	20÷4=5 or 20/4=5
±	Plus-minus	plus or minus	x±y means both x+y and x-y	1±2 represents both 3 and -1
∓	Minus-plus	minus or plus	4±(3∓5) means both 4+(3-5) and 4-(3+5)	6∓(1±3)=2 or 4
√	Square root	square root	√x is a nonnegative number whose square is x.	√4=2
∑	Summation	sum over … from … to … of, beta	${\displaystyle \sum _{k=1}^{n}{x_{k}}}$ is the same as x1+x2+x3+...+xn	${\displaystyle \sum _{k=1}^{5}{(k+2)}=3+4+5+6+7=25}$
∏	Product	product over … from … to … of	${\displaystyle \prod _{k=1}^{n}{x_{k}}}$ is the same as x1×x2×x3×....×xn	${\displaystyle \prod _{k=1}^{5}{k}}$=1×2×3×4×5=120
!	Factorial	factorial	n! is the product 1×2×3...×n	5!=1×2×3×4×5=120
⇒	Material implication	implies	A⇒B means that if A is true, B must also be true, but if A is false, B is unknown.	x=3⇒x2=9, but x2=9⇒x=3 is false, because x could also be -3.
⇔	Material equivalence	if and only if	If A is true, B is true and if A is false, B is false.	x=y+1⇔x-1=y
|…|	Absolute value	absolute value of	|x| is the distance along the real line (or across the complex plane) between x and zero.	|x|=x and |-x|=x
||	Parallel	is parallel to	If A||B then line A will never touch line B, thus both lines are rotated in the same angle.	x||(x+1)
⊥	Perpendicular	is perpendicular to	If A⊥B then line A is touching line B in a 90 degrees angle.	x⊥y
≅	Congruence	is congruent to	If A≅B then shape A and B same shape and size, or A has the same shape and size as the mirror image of B.	If two triangles, △ABC and △DEF, are congruent, it can be denoted as △ABC≅△DEF
φ	Golden ratio	golden ratio	The golden ratio is an irrational number equal to (1+√5)÷2 or approximately 1.6180339887.	φ ≈ 1.6180339887
∞	Infinity	infinity	∞ is a symbol used to represent unending amounts.	∞ + x = ∞
∈	Set membership	is an element of	a∈S means that a is an element of the set S	3.5∈ℝ, 1∈ℕ, 1+i∈ℂ
∉		is not an element of	a∉S means that a is not an element of the set S	2.1∉ℕ, 1+i∉ℝ
{,}	Set brackets	the set of	{a,b,c} is the set consisting of a, b, and c	S = { a, b, c }
ℕ	Natural numbers	N	ℕ denotes the set of natural numbers	1∈ℕ, 2∈ℕ, 100∈ℕ
ℤ	Integers	Z	ℤ denotes the set of integers	-1∈ℤ, 0∈ℤ, 30∈ℤ
ℚ	Rational numbers	Q	ℚ denotes the set of rational numbers	8.323∈ℚ, 7∈ℚ, π∉ℚ
ℝ	Real numbers	R	ℝ denotes the set of real numbers	π∈ℝ, 7∈ℝ, √(-1)∉ℝ
ℂ	Complex numbers	C	ℂ denotes the set of complex numbers	√(-1)∈ℂ
x̄	Mean	bar, overbar	x̄ is the mean (average) of xi	if x={1,2,3} then x̄=2
x̄	Complex conjugate	the complex conjugate of x	If x=a ± bi, then x̄=a ∓ bi where i=√(-1)	x=-4 + 5.3i, x̄=-4 - 5.3i
[+|-]	Situational plus minus	Either plus or minus depending on the situation.	If y=[+|-]x then x is either positive or negative depending on the situation.	y=[+|-]x y equals either +x or -x depending on the scenario.
π	Irrational numbers	pi

Related page

• Mathematical constant

Other websites

• Mathematical Symbols — Math Vault
• Math Symbols List —