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 |
≥ | 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 number whose square is x. | √4=2 or -2 |
∑ | summation | sum 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} |
∏ | multiplication | product 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 |
! | 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={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 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 |
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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 Symbol | Mathematics 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+2102 | ℂ | Represents 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 | ⅅ | ||
U+2146 | ⅆ | May 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+2147 | ⅇ | Occasionally 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+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 | ? | ||
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+2148 | ⅈ | Occasionally used for the imaginary unit. | |
U+1D541 | ? | Occasionally represents the set of irrational numbers, R\Q (ℝ\ℚ). | |
U+1D55B | ? | ||
U+2149 | ⅉ | ||
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 ?(m, n). | |
U+1D55E | ? | ||
U+2115 | ℕ | Represents the set of natural numbers. May or may not include zero. | |
U+1D55F | ? | ||
U+1D546 | ? | Represents the octonions. | |
U+1D560 | ? | ||
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 | ? | ||
U+211A | ℚ | Represents the set of rational numbers. (The Q stands for quotient.) | |
U+1D562 | ? | ||
U+211D | ℝ | Represents 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+2124 | ℤ | Represents the set of integers. (The Z is for Zahlen, German for “numbers”, and zählen, German for “to count”.) |
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