List of mathematical symbols

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This list provides a list of mathematical symbols. Table is based on the one onList of mathematical symbols.

Symbol	Name	Read as	Meaning	Example
=	equality	equals, is equal to	If x=y, x and y represent the same value or thing.	2+2=4
≡	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. (Note: "~" is usually used for rough approximations, and "≈" for close approximations)	π≈3.14159 π~3
≠	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.	88979808≫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
√	positive square root	positive square root	√x is a non-negative number whose square is x.	√4=2
∑	summation	sum over … from … to … of, sigma	$\sum_{k=1}^{n}{x_k}$ is the same as x1+x2+x3+...+xk	$\sum_{k=1}^{5}{k+2}=3+4+5+6+7=25$
∏	multiplication	product over … from … to … of	$\prod_{k=1}^{n}{x_k}$ is the same as x1×x2×x3×...×xk	$\prod_{k=1}^{5}{k}$=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 number greater than every real number.
∈	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={1,2,3,4,5,....}
ℕ	Natural numbers	N	ℕ denotes the set of natural numbers {1,2,3,4,5...} Note: Some authors define the set of natural numbers to be {0,1,2,3,4,5,...}
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

References

This article is part of Project Maths, a All Birds project that aims to write comprehensive articles on each term related to mathematics.