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1. Arithmetic Symbols
+
(Addition)
-
(Subtraction)
×
or *
(Multiplication)
÷
or /
(Division)
=
(Equals)
≠
(Not equal to)
≡
(Identical to)
≈
(Approximately equal to)
±
(Plus-minus)
∓
(Minus-plus)
∗
(Star product, used in various contexts)
//
(Integer division)
2. Relational and Comparison Symbols
<
(Less than)
>
(Greater than)
≤
(Less than or equal to)
≥
(Greater than or equal to)
≠
(Not equal to)
≡
(Identical to)
≈
(Approximately equal to)
3. Set Theory Symbols
{ }
(Set brackets)
∅
(Empty set)
∈
(Element of)
∉
(Not an element of)
⊂
(Subset of)
⊆
(Subset or equal to)
⊄
(Not a subset of)
⊇
(Superset or equal to)
⊃
(Superset of)
∪
(Union)
∩
(Intersection)
∖
(Set difference)
×
(Cartesian product)
4. Logic and Propositional Symbols
∧
(Logical AND)
∨
(Logical OR)
¬
(Negation)
→
(Implies)
↔
(If and only if)
⊥
(Contradiction)
⊤
(Tautology)
5. Calculus Symbols
∂
(Partial derivative)
∫
(Integral)
∮
(Contour integral)
∞
(Infinity)
∑
(Summation)
Π
(Product)
lim
(Limit)
d/dx
(Derivative with respect to x)
6. Algebraic Symbols
√
(Square root)
∛
(Cube root)
∜
(Fourth root)
x²
(x squared)
x³
(x cubed)
n!
(Factorial of n)
|x|
(Absolute value of x)
±
(Plus-minus sign)
7. Geometry Symbols
⊥
(Perpendicular to)
∥
(Parallel to)
∠
(Angle)
∡
(Measure of angle)
Δ
(Delta, used for change or triangle)
∘
(Degree)
∭
(Triple integral)
8. Number Theory Symbols
ℕ
(Natural numbers)
ℤ
(Integers)
ℚ
(Rational numbers)
ℝ
(Real numbers)
ℂ
(Complex numbers)
ℍ
(Quaternions)
⊙
(Circled dot, used in different number theory contexts)
9. Probability and Statistics Symbols
P(A)
(Probability of event A)
E(X)
(Expected value of random variable X)
Var(X)
(Variance of X)
σ
(Standard deviation)
μ
(Mean or population mean)
Σ
(Summation)
∼
(Distributed as)
∠
(Angle)
|A|
(Cardinality of set A)
10. Matrix and Vector Symbols
A₁
(Element of matrix A)
⟦A⟧
(Matrix brackets)
→
(Vector arrow)
∥A∥
(Norm of matrix A)
det(A)
(Determinant of matrix A)
Tr(A)
(Trace of matrix A)
11. Miscellaneous Symbols
°
(Degree, angle measurement)
∽
(Similar to)
⊕
(Direct sum or exclusive OR)
⊗
(Tensor product or Kronecker product)
⋅
(Dot product)
◯
(Circle, sometimes used for operations)
∞
(Infinity)
∑
(Summation)
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