# 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:

– (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

=
equalityequals, is equal toIf x=y, x and y represent the same value or thing.2+3=5
definitionis defined asIf x≡y, x is defined as another name of y(a+b)2≡a2+2ab+b2
approximately equalis approximately equal toIf x≈y, x and y are almost equal.√2≈1.41
inequationdoes not equal, is not equal toIf x≠y, x and y do not represent the same value or thing.1+1≠3
<
strict inequality
is less thanIf x<y, x is less than y.4<5
>
is greater thanIf x>y, x is greater than y.3>2
is much less thanIf x≪y, x is much less than y.1≪999999999
is much greater thanIf x≫y, x is much greater than y.88979808≫0.001
inequality
is less than or equal toIf x≤y, x is less than or equal to y.5≤6 and 5≤5
is greater than or equal toIf x≥y, x is greater than or equal to y.2≥1 and 2≥2
proportionalityis proportional toIf x∝y, then y=kx for some constant k.If y=4x then y∝x and x∝y
+
additionplusx+y is the sum of x and y.2+3=5
subtractionminusx-y is the subtraction of y from x5-3=2
×
multiplicationtimesx×y is the multiplication of x by y4×5=20
·
x·y is the multiplication of x by y4·5=20
÷
divisiondivided byx÷y or x/y is the division of x by y20÷4=5 and 20/4=5
/
20/4=5
±
plus-minusplus or minusx±y means both x+y and x-yThe equation 3±√9 has two solutions, 0 and 6.
minus-plusminus or plus4±(3∓5) means both 4+(3-5) and 4-(3+5)6∓(1±3)=2 or 4
square rootsquare root√x is a number whose square is x.√4=2 or -2
summationsum over … from … to … of, sigma{\displaystyle \sum _{k=1}^{n}{x_{k}}} is the same as x1+x2+x3+xk{\displaystyle \sum _{k=1}^{5}{k+2}=3+4+5+6+7=25} multiplicationproduct over … from … to … of{\displaystyle \prod _{k=1}^{n}{x_{k}}} is the same as x1×x2×x3×xk{\displaystyle \prod _{k=1}^{5}{k}} =1×2×3×4×5=120
!
factorialfactorialn! is the product 1×2×3…×n5!=1×2×3×4×5=120
material implicationimpliesA⇒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 equivalenceif and only ifIf A is true, B is true and if A is false, B is false.x=y+1⇔x-1=y
|…|
absolute valueabsolute value of|x| is the distance along the real line (or across the complex plane) between x and zero|5|=5 and |-5|=5
||
parallelis parallel toIf A||B then A and B are parallel
perpendicularis perpendicular toIf A⊥B then A is perpendicular to B
congruenceis congruent toIf A≅B then shape A is congruent to shape B (has the same measurements)
φ
golden ratiogolden ratioThe golden ratio is an irrational number equal to (1+√5)÷2 or approximately 1.6180339887.
infinityinfinity∞ is a number greater than every real number.
set membershipis an element ofa∈S means that a is an element of the set S3.5∈ℝ, 1∈ℕ, 1+i∈ℂ
is not an element ofa∉S means that a is not an element of the set S2.1∉ℕ, 1+i∉ℝ
{,}
Set bracketsthe set of{a,b,c} is the set consisting of a, b, and cℕ={0,1,2,3,4,5…}
Natural numbersNℕ denotes the set of natural numbers {0,1,2,3,4,5…}
IntegersZℤ denotes the set of integers (-3,-2,-1,0,1,2,3…)
Rational numbersQℚ 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
Real numbersRℝ denotes the set of real numbersπ∈ℝ, 7∈ℝ, √(-1)∉ℝ
Complex numbersCℂ denotes the set of complex numbers√(-1)∈ℂ
Meanbar, overbarx̄ is the mean (average) of xiif x={1,2,3} then x̄=2
complex conjugatethe complex conjugate of xIf 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. Unicode Code Point (Hex)Unicode SymbolMathematics usage 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? U+1D539?Sometimes represents a ball, a boolean domain, or the Brauer group of a field.
U+1D553? U+2102Represents the set of complex numbers.
U+1D554? 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? U+2145 U+2146May represent the differential symbol. 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? U+2147Occasionally used for the mathematical constant e. 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? U+1D53E?Represents a Grassmannian or a group, especially an algebraic group.
U+1D558? U+210DRepresents the quaternions (the H stands for Hamilton), or the upper half-plane, or hyperbolic space, or hyperhomology of a complex.
U+1D559? 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? U+2148Occasionally used for the imaginary unit. U+1D541?Occasionally represents the set of irrational numbers, R\Q (ℝ\ℚ).
U+1D55B? U+2149 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. U+1D55C? U+1D543?Represents the Lefschetz motive. See Motive (algebraic geometry).
U+1D55D? U+1D544?Sometimes represents the monster group. The set of all m-by-n matrices is sometimes denoted ?(mn).
U+1D55E? U+2115Represents the set of natural numbers. May or may not include zero.
U+1D55F? U+1D546?Represents the octonions.
U+1D560? U+2119Represents projective space, the probability of an event, the prime numbers, a power set, the irrational numbers, or a forcing poset.
U+1D561? U+211ARepresents the set of rational numbers. (The Q stands for quotient.)
U+1D562? U+211DRepresents the set of real numbers. {\displaystyle \mathbb {R} _{>0}} represents the positive reals, while {\displaystyle \mathbb {R} _{\geq 0}} represents the non-negative real numbers.
U+1D563? U+1D54A?Represents a sphere, or the sphere spectrum, or occasionally the sedenions.
U+1D564? 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 Tn or ??), or the tropical semi-ring, or twistor space.
U+1D565? U+1D54C?
U+1D566? U+1D54D?Represents a vector space or an affine variety generated by a set of polynomials.
U+1D567? 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? U+1D54F?Occasionally used to denote an arbitrary metric space.
U+1D569? U+1D550?
U+1D56A? U+2124Represents the set of integers. (The Z is for Zahlen, German for “numbers”, and zählen, German for “to count”.)