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.

Symbol	Name	Read as	Meaning	Example(s)
=	Equality	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 less than	If x<y, x is less than y.	4<5
>		is 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 or equal to	If x≤y, x is less than or equal to y.	5≤6 and 5≤5
≥		is greater than or equal to	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 ·	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 /	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, sigma	${\displaystyle \sum _{k=1}^{n}{x_{k}}}$ 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.