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.

These are symbols that is most commonly used in linear algebra.

Name	Read as	Description	Meaning	Example(s)
=	equality	equals, is equal to	If x=y, x and y represent the same value or thing.	2+3=5
≡	definition	is defined as	If x≡y, x is defined as another name of y	(a+b)2≡a2+2ab+b2
≈	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.	1≪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
×	multiplication	times	x×y is the multiplication of x by y	4×5=20
·			x·y is the multiplication of x by y	4·5=20
÷	division	divided by	x÷y or x/y is the division of x by y	20÷4=5 and 20/4=5
/				20/4=5
±	plus-minus	plus or minus	x±y means both x+y and x-y	The equation 3±√9 has two solutions, 0 and 6.
∓	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	${\displaystyle \sum _{k=1}^{5}{(k+2)}=3+4+5+6+7=25}$
∏	multiplication	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	|5|=5 and |-5|=5
||	parallel	is parallel to	If A||B then A and B are parallel
⊥	perpendicular	is perpendicular to	If A⊥B then A is perpendicular to B
≅	congruence	is congruent to	If A≅B then shape A is congruent to shape B (has the same measurements)
φ	golden ratio	golden ratio	The golden ratio is an irrational number equal to (1+√5)÷2 or approximately 1.6180339887.
∞	infinity	infinity	∞ is a symbol used to represent unending amounts.
∈	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	ℕ={0,1,2,3,4,5...}
ℕ	Natural numbers	N	ℕ denotes the set of natural numbers {0,1,2,3,4,5...} (0 may or may not be included as natural number)
ℤ	Integers	Z	ℤ denotes the set of integers (-3,-2,-1,0,1,2,3...)
ℚ	Rational numbers	Q	ℚ denotes the set of rational numbers (numbers that can be written as a fraction a/b where a∈ℤ, b∈ℕ)	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.