Math Symbol | What Does This Symbol Mean in Mathematics?

cleverlysmart.com January 25, 2021 in Mathematics - 14 Minutes

Math Symbol

A math symbol or mathematical symbol is a figure that is used to represent action, relation, on mathematical objects or for structuring the other symbols that occur in a formula. As formulas are entierely constitued with symbols of various types, many symbols are needed for expressing all mathematics.

Here are a list of symbols supported by Algebra Calculator:

+ (Addition)
– (Subtraction)
* (Multiplication)
/ (Division)
^ (Exponent: “raised to the power”)
sqrt (Square Root) (Example: sqrt(9))
< (less than) > (greater than)
<= (less than or equal to) >= (greater than or equal to)

Table of Math Symbol

Symbol	Name	Read as	Meaning	Example
=	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.	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
≥	inequality	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
·	multiplication	times	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
/	division	divided by	x÷y or x/y is the division of x by y	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 number whose square is x.	√4=2 or -2
∑	summation	sum over … from … to … of, sigma	$\sum _{k=1}^{n}{x_{k}}$ is the same as x₁+x₂+x₃+x_k	$\sum _{k=1}^{5}{k+2}=3+4+5+6+7=25$
∏	multiplication	product over … from … to … of	$\prod _{k=1}^{n}{x_{k}}$ is the same as x₁×x₂×x₃×x_k	$\prod _{k=1}^{5}{k}$ =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
∉	set membership	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…}
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 x_i	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

Math Symbol (Unicode math symbol)

The first column shows the letter as typically rendered by the ubiquitous LaTeX markup system. The second column shows the Unicode code point. The third column shows the Unicode symbol itself (which will only display correctly on browsers that support Unicode and have access to a suitable font). The fourth column describes known typical (but not universal) usage in mathematical texts.

$\LaTeX$	Unicode Code Point (Hex)	Unicode Symbol	Mathematics usage
$\mathbb {A}$	`U+1D538`	?	Represents affine space or the ring of adeles. Occasionally represents the algebraic numbers, the algebraic closure of ℚ (more commonly written ℚ or Q), or the algebraic integers, an important subring of the algebraic numbers.
	`U+1D552`	?
$\mathbb {B}$	`U+1D539`	?	Sometimes represents a ball, a boolean domain, or the Brauer group of a field.
	`U+1D553`	?
$\mathbb {C}$	`U+2102`	ℂ	Represents the set of complex numbers.
	`U+1D554`	?
$math symbol \mathbb {D}$	`U+1D53B`	?	Represents the unit (open) disk in the complex plane (and by generalisation ?ⁿ may mean the n-dimensional ball) — for example as a model of the Hyperbolic plane and the domain of discourse. Occasionally the math symbol ? may mean the decimal fractions (see number) or split-complex numbers.
	`U+1D555`	?
$D\!\!\!\!D$	`U+2145`	ⅅ
$\,d\!\!\!\!d$	`U+2146`	ⅆ	May represent the differential symbol.
$\mathbb {E}$	`U+1D53C`	?	Represents the expected value of a random variable, or Euclidean space, or a field in a tower of fields, or the Eudoxus reals.
	`U+1D556`	?
$e\!\!e$	`U+2147`	ⅇ	Occasionally used for the mathematical constant $e$ .
$\mathbb {F}$	`U+1D53D`	?	Represents a field. Often used for finite fields, with a subscript to indicate the order. Also represents a Hirzebruch surface or a free group, with a subset to indicate the number of generators (or generating set, if infinite).
	`U+1D557`	?
$math symbol \mathbb {G}$	`U+1D53E`	?	Represents a Grassmannian or a group, especially an algebraic group.
	`U+1D558`	?
$\mathbb {H}$	`U+210D`	ℍ	Represents the quaternions (the H stands for Hamilton), or the upper half-plane, or hyperbolic space, or hyperhomology of a complex.
	`U+1D559`	?
$\mathbb {I}$	`U+1D540`	?	The closed unit interval or the ideal of polynomials vanishing on a subset. Occasionally the identity mapping on an algebraic structure, or an indicator function, or the set of imaginary numbers (i.e., the set of all real multiples of the imaginary unit, more commonly indicated iℝ)
	`U+1D55A`	?
$i\!i$	`U+2148`	ⅈ	Occasionally used for the imaginary unit.
$\mathbb {J}$	`U+1D541`	?	Occasionally represents the set of irrational numbers, R\Q (ℝ\ℚ).
	`U+1D55B`	?
$j\!\!j$	`U+2149`	ⅉ
$\mathbb {K}$	`U+1D542`	?	Represents a field, typically a scalar field. This is derived from the German word Körper, which is German for field (literally, “body”; cf. the French term corps). May also be used to denote a compact space.
$\mathbb {k}$	`U+1D55C`	?
$\mathbb {L}$	`U+1D543`	?	Represents the Lefschetz motive. See Motive (algebraic geometry).
	`U+1D55D`	?
$\mathbb {M}$	`U+1D544`	?	Sometimes represents the monster group. The set of all m-by-n matrices is sometimes denoted ?(m, n).
	`U+1D55E`	?
$\mathbb {N}$	`U+2115`	ℕ	Represents the set of natural numbers. May or may not include zero.
	`U+1D55F`	?
$\mathbb {O}$	`U+1D546`	?	Represents the octonions.
	`U+1D560`	?
$\mathbb {P}$	`U+2119`	ℙ	Represents projective space, the probability of an event, the prime numbers, a power set, the irrational numbers, or a forcing poset.
	`U+1D561`	?
$\mathbb {Q}$	`U+211A`	ℚ	Represents the set of rational numbers. (The Q stands for quotient.)
	`U+1D562`	?
$\mathbb {R}$	`U+211D`	ℝ	Represents the set of real numbers. ${\mathbb {R}}_{{>0}}$ represents the positive reals, while $\mathbb {R} _{\geq 0}$ represents the non-negative real numbers.
	`U+1D563`	?
$\mathbb {S}$	`U+1D54A`	?	Represents a sphere, or the sphere spectrum, or occasionally the sedenions.
	`U+1D564`	?
$\mathbb {T}$	`U+1D54B`	?	Represents the circle group, particularly the unit circle in the complex plane (and ?ⁿ the n-dimensional torus), or a Hecke algebra (Hecke denoted his operators as T_n or ?_?), or the tropical semi-ring, or twistor space.
	`U+1D565`	?
$\mathbb {U}$	`U+1D54C`	?
	`U+1D566`	?
$\mathbb {V}$	`U+1D54D`	?	Represents a vector space or an affine variety generated by a set of polynomials.
	`U+1D567`	?
$math symbol \mathbb {W}$	`U+1D54E`	?	Occasionally represents the set of whole numbers (here in the sense of non-negative integers), which also are represented by ℕ₀.
	`U+1D568`	?
$\mathbb {X}$	`U+1D54F`	?	Occasionally used to denote an arbitrary metric space.
	`U+1D569`	?
$\mathbb {Y}$	`U+1D550`	?
	`U+1D56A`	?
$\mathbb {Z}$	`U+2124`	ℤ	Represents the set of integers. (The Z is for Zahlen, German for “numbers”, and zählen, German for “to count”.)