In the language of Mathematics, there are many strange symbols that can complicate papers and proofs for those without knowledge of them (take the Standard Model Lagrangian equation, for example). In this page I will collect every strange Mathematical or Physics-related symbol that I come across in my studies. NOTE: This is not inclusive of electrical engineering circuitry symbols or those of any other discipline. E.E. symbols are found here.
In the unlikely event there are any egregious errors in this page, contact me at jdlacabe@gmail.com.
Mathematical Symbols
Table Of Contents
Non-Constant Symbols.
+
The plus sign. A symbol for addition in arithmetic.Example: 5 + 906 = 911
-
The minus sign. The symbol for subtraction in arithmetic. It is the opposite of the plus sign and can also denote negative numbers.Examples: 20 - 5 = 15
-7 - 12 = -19
×, •
The multiplication symbol. The symbol denoting multiplying two numbers together. Can also be represented using a dot.Examples: 3 × 5 = 15
-1 • 0 = 0
÷, /
The division symbol. The symbol denoting division, the opposite of multiplication. It can also be represented using a slash.Example: 21 ÷ 3 = 7
±
Plus-Minus. Denotes that a number can be either positive or negative. It can also be used to denote a range of values, such as 5±3 having a range from 2 to 8.Example: 2 ± 1 = 1, 3
∓
Minus-Plus. A symbol used in conjunction with the plus-minus sign to denote the opposite sign of plus-minus.Example: 1 ± 2 ∓ 3 = 1 + 2 - 3 OR 1 - 2 + 3, not anything else.
=
Equals. A symbol denoting equality between two expressions.Example: 1 + 2 = 3
≠
The not equals sign. The opposite of the equals sign, indicating that two expressions are not equal.Example: 6 + 2 ≠ 3
≈
The approximately equals sign. Used when 2 values are not eactly equal but are close enough. A tilde can also be used, but it has other specialized purposes as well.Example: 12.00910239012931 + 1.999923891273 ≈ 14
~
Tilde. A symbol that indicates proportionality/similarity between two geometric figures. Image.Example: ABC ~ DEF
∝
The proportional symbol. Can be used for more explicit reference to proportionality in place of ~.Example: y = k × x, and thus y ∝ x.
≡
The Triple Bar or Equivalence Bar. Used to denote an identity or definition, commonly used in modular arithmetic (see Cryptography).Example: 22 ≡ 2(mod 10)
√
The square root. Denotes the square root of a number, e.g. what number multiplied by itself gives x. Additional roots exist as well, with an integer greater than two serving as n as the superscript to the left of the root symbol: n√x. This denotes the nᵗʰ root of x.Example: 1 + 2 = 3
<
The less-than symbol. Used to indicate that one quantity is smaller than another.Example: 0.99999 < 1
>
The greater than sign. Indicates that one quantity is larger than the other. It is the opposite of the less-than sign.Example: 8 > 5
≤
The less than or equal to symbol. Indicates that one value is smaller or equal to another.Example: 2 ≤ 9
2 ≤ 2
≥
The greater than or equal to symbol. Indicates that one value is greater or equal to another.Example: 13 ≥ 1
13 ≥ 13
≪
The much less than sign. Denotes one value is much smaller than the other.Example: 0.02 ≪ 10000
≫
The much greater than sign. Denotes one value is much greater than the other.Example: 20349823 ≫ 3
||x||
The Magnitude. Simply represents the magnitude of a particular value, the directionless 'amount' of something.Example: ||a|| = -9.81 m/s²
θ
Theta. Used as the primary variable to represent an angle.Example: In a right triangle, θ₁ + θ₂ + θ₃ = 180°.
Φ
Phi. An alternate angle symbol, oftentimes used when theta is already taken by another angle.Example: tan(Φ) = (sin(Φ) / cos(Φ))
∅
An empty set. Denotes a set that contains no elements.Example: ∅ = {}
#
The number sign, also known as the pound sign, octothorpe, or hashtag. This denotes the cardinality of the set, e.g. the number of elements in the set.Example: P = {2, 4, 5}
#P = 3
∈
The element symbol, also known as the member symbol. Used to denote membership of an object in a set.Example: 2 ∈ P
∉
The not element of symbol, or not member of symbol. It denotes that an element is not a member of a set.Example: 8 ∉ P
⊂
The set inclusion sign. Denotes that one set is a subset of another set.Example: P = {2, 4, 5}
Q = {4, 5}
R = {4, 5}
Q ⊂ P
⊆
The set inclusion sign (but more specific and used than the one above). Denotes set inclusion, in addition to emphasizing that the sets can be equal.Example: P = {2, 4, 5}
Q = {4, 5}
R = {4, 5}
Q ⊆ P
⊊
The proper subset symbol. Denotes set inclusion where the sets are not equal.Example: P = {2, 4, 5}
Q = {4, 5}
R = {4, 5}
R ⊂ P
∪
The Union symbol. Denotes an operation of combining two sets, which results in another set containing all unique elements from both sets. Oftentimes, it is used to combine intervals on a graph for some purpose, such as where x is increasing or decreasing.Example: A = {2, 3, 4, 5}
B = {3, 5, 6, 7}
A ∪ B = {2, 3, 4, 5, 6, 7}
∩
The intersection symbol. Denotes an operation of combining 2 sets, the result of intersection is a set which contains elements that are common in both sets.Example: A = {2, 3, 4, 5}
B = {3, 5, 6, 7}
A ∩ B = {3, 5}
\
The set difference symbol. Denoted by a backslash, the result of this operation is a set which contains all elements of the first set that are not in the second set.Example: A = {2, 3, 4, 5}
B = {3, 5, 6, 7}
A \ B = {2, 4}
Δ
The delta symbol, represents 'the change in' some value. For example: Δx represents the displacement, or change in position of some value - see here for a more detailed explanation. It is occasionally used interchangeably with ⊖ for symmetric differences.Example: y = x + 5 has a Δx of 5.
ω
The angular velocity in rotational motion.Example: ωavg = (∆θ / ∆t)
α
Alpha. Can be used to represent angular acceleration.Example: α = ((ωF - ωi) / ∆t)
⊖
The symmetric difference symbol. Denotes an operation which creates a set of all elements that belong to exactly one of the 2 sets. Can also be represented using Δ.Example: A = {2, 3, 4, 5}
B = {3, 5, 6, 7}
A ⊖ B = {2, 4, 6, 7}
¬
The negation symbol. Used in logic to indicate the opposite of a statement.Example: P = false
¬P = true
∨
The "or" operator. Returns true if at least one of the operands is true. It works akin to the || operator in programming.Example: P = false, Q = true
P ∨ Q = true
∧
The "and" operator. Returns true only if both operands are true. It works akin to the && operator in programming.Example: P = false, Q = true
P ∨ Q = false
⊕
The "Exclusive or" operator. Returns true if exactly one of the operands is true. Is also known as an XOR gate.Example: P = false, Q = true
P ⊕ Q = true
⊤
The "Tee". Denotes the logical constant for a true value or a statement that is always true.Example: R ∨ ¬R = ⊤
⊥
Uptack. Denotes the logical constant for a false value or a statement that is always false.Example: 1 + 2 = 3
∀
The Universal Quantifier. Asserts that a statement is true for all elements in a given domain.Example: ∀n ∈ ℕ (2n ≥ n)
"For all natural numbers n, 2n is greater or equal to n"
∃
The Existential Quantifier. Asserts that there exists at least one element in a given domain for which a particular statement holds true.Example: ∃x (x > 5)
"There exists at least one number x that is bigger than 5"
∃!
The Uniqueness Quantifier. Used to assert that there is exactly one element in a given domain for which a particular statement holds true.Example: ∃!n ∈ ℕ (n = 5)
"There exists exactly one natural number n that is equal to 5"
⇒
The conditional operator. Denote an implication between 2 statements. If the first element is true, then the second is also trueExample: x > 2 ⇒ x >1
"If x is bigger than 2, then x is also bigger than 1"
⟺
The logical equivalence symbol. Indicates that 2 statements have the same logical value.Example: x = 0 ⟺ x² = 0
"x is equal to 0 if and only if x² is also equal to 0"
⨍′
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
ẋ
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
df/dx
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∂f/∂x
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∫
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
↦
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∘
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
log
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
ln
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
lim
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
ℜ
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
ℑ
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
x̄
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
Σ
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∏
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∞
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
ℵ
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
𝔠
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
!
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
Example: 1 + 2 = 3
|x|
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
⌊x⌋
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
⌈x⌉
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
⌊x⌉
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
|
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∤
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∥
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∦
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
⊥
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
AB
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
AB
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
AB
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
Blackboard Bold Typeface
These symbols typically denote the basic number systems. Generally, you would not consider ∞ to be a member of any of these sets, as they are all defined to not have a largest element and ∞ is defined as being greater than any element.ℕ
The set of a natural numbers. All positive whole numbers.Example: 1 ∈ ℕ
1.01 ∉ ℕ
0 ∉ ℕ
ℤ
The set of integers. Any whole number, positive or negative.Example: 1 ∈ ℤ
-4 ∈ ℤ
-0.1 ∉ ℤ
ℚ
The set of rational numbers. Any number that can be represented as a fraction of whole numbers, positive or negative.Example: 1 ∈ ℚ
-1/12 ∈ ℚ
e ∉ ℚ
ℝ
The set of real numbers. The set of numbers that includes both rational and irrational numbers, without regard for whole numbers.Example: 0 ∈ ℝ
π ∈ ℝ
√-1 ∉ ℝ
ℂ
The set of complex numbers. Incorporates real numbers and imaginary numbers into one set.Example: e ∈ ℕ
√-1 ∈ ℕ
∞ ∉ ℕ
ℍ
The set of quaternions.Example: 1 ∈ ℕ
1.01 ∉ ℕ
0 ∉ ℕ
𝕆
The set of octonions.Example: 1 ∈ ℕ
1.01 ∉ ℕ
0 ∉ ℕ
𝕌
The Universal set, the set that contains all possible values.Example: 1 ∈ ℕ
1.01 ∉ ℕ
0 ∉ ℕ
Constants.
π
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
τ
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
e
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
i
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
ψ
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
φ
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
δS
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
ρ
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
α
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
θm
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
Tribonacci Constant
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
Viswanath's constant
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
β*
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
√2
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
L
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
K0
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
γ
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
M
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
B
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
Ω
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
eπ
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
2√2
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
C
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
G
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
ζ(3)
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
Wallis Product
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
σ
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
MRB constant
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
B2
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
B4
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
C
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∦
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∦
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∦
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∦
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∦
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∦
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∦
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∦
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∦
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∦
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
∦
A symbol denoting equality between two expressions.Example: 1 + 2 = 3
