+ (Addition): Adds two numbers or quantities. It's one of the most fundamental operations in mathematics. Example: 3 + 5 = 8. Addition is also used in combining vectors and adding functions.
- (Subtraction): Finds the difference between two numbers. Also essential in balancing equations and algebra. Example: 8 - 3 = 5.
× (Multiplication): Repeated addition. It also represents scaling in linear algebra. Example: 4 × 2 = 8.
÷ (Division): Splits a number into equal parts or groups. In fractional notation, it's represented as a fraction bar (e.g., 6 ÷ 3 = 2 or 6/3 = 2).
= (Equals): Shows equivalence. It's pivotal in forming equations and proving mathematical theorems. Example: x + 2 = 4.
≠ (Not Equal): Indicates non-equivalence, crucial in inequalities. Example: 3 ≠ 5.
Greater Than (>): Compares two values and denotes the larger one. Example: 7 > 4.
Less Than (<): Compares two values and denotes the smaller one. Example: 2 < 5.
∠ (Angle): Represents the measure of rotation between two intersecting lines or segments. It's measured in degrees or radians. Example: ∠ABC = 45°.
△ (Triangle): Denotes a shape with three sides. Properties of triangles are central to trigonometry. Example: △ABC.
∥ (Parallel): Indicates lines that never meet. Example: Line l₁ is parallel to line l₂ (l₁ ∥ l₂).
⊥ (Perpendicular): Represents lines that intersect at 90°. Example: AB ⊥ CD.
∈ (Belongs to): Indicates that an element is part of a set. Example: x ∈ {1, 2, 3}.
∉ (Does Not Belong To): Opposite of ∈. Example: 4 ∉ {1, 2, 3}.
⊆ (Subset): A set whose elements are entirely within another set. Example: {1, 2} ⊆ {1, 2, 3}.
⊇ (Superset): A set that contains another set entirely. Example: {1, 2, 3} ⊇ {1, 2}.
∫ (Integral): Represents accumulation, like areas under curves. In physics, it measures quantities like energy and flux. Example: ∫₀¹ x² dx = 1/3.
Σ (Summation): Adds up a sequence of terms. Essential in series. Example: Σ(i=1 to n) i = n(n + 1)/2.
lim (Limit): Describes the behavior of a function as it approaches a point. Example: lim(x → 0) (sin x / x) = 1.
∂ (Partial Derivative): Measures changes in multivariable functions with respect to one variable. Example: ∂f/∂x.
sin: Function of an angle in a right triangle, defined as the ratio of the opposite side to the hypotenuse. Example: sin(30°) = 0.5.
cos: Ratio of the adjacent side to the hypotenuse. Example: cos(30°) = √3/2.
tan: Ratio of the opposite side to the adjacent side. Example: tan(45°) = 1.
∞ (Infinity): Denotes an unbounded value or concept. Example: The sequence 1/n approaches 0 as n approaches ∞.
π (Pi): Represents the ratio of a circle's circumference to its diameter. Example: π ≈ 3.14159.
√ (Square Root): Indicates the value that, when squared, equals the given number. Example: √9 = 3.
∛ (Cube Root): Represents the value that, when cubed, equals the given number. Example: ∛8 = 2.
Θ (Theta): A Greek letter often used to represent angles in trigonometry or asymptotic behavior in mathematics and computer science. Example: Θ(n²) represents quadratic time complexity.