Understanding and interpreting mathematical symbols, expressions, and equations commonly used in scientific disciplines.
Introduction to Mathematical Notation
Key ideas, symbols, and conventions that make mathematics precise and concise.
| Symbol | Name | Typical Meaning | Example |
|---|---|---|---|
= |
Equality | Two expressions represent the same object | 3 + 4 = 7 |
≠ |
Inequality | Two expressions are not equal | x ≠ 0 |
+ , – , × , ÷ |
Arithmetic operations | Addition, subtraction, multiplication, division | a + b, c·d, e / f |
^ |
Exponentiation | Power of a number | x^2 = “x squared” |
√ |
Square root | Principal square root | √9 = 3 |
∑ |
Summation | Sum of a sequence of terms | ∑_{k=1}^{n} k = n(n+1)/2 |
∏ |
Product | Product of a sequence of terms | ∏_{k=1}^{n} k = n! |
∈ |
Element of | Membership in a set | 3 ∈ ℕ |
⊂ , ⊆ |
Subset, Subset‑or‑equal | Set containment | ℕ ⊂ ℤ |
∪ , ∩ |
Union, Intersection | Set operations | A ∪ B, A ∩ B |
→ |
Function arrow | Maps input to output | f: ℝ → ℝ, f(x) = x^2 |
↔ |
Logical equivalence | Two statements have the same truth value | P ↔ Q |
∧ , ∨ , ¬ |
Logical AND, OR, NOT | Connectives in propositional logic | P ∧ Q, ¬P |
∀ |
Universal quantifier | “For all” | ∀x ∈ ℝ, x^2 ≥ 0 |
∃ |
Existential quantifier | “There exists” | ∃x ∈ ℝ, x^2 = 4 |
∂ |
Partial derivative | Derivative with respect to one variable in a multivariable function | ∂f/∂x |
∇ |
Nabla / Gradient | Vector of partial derivatives | ∇f = (∂f/∂x, ∂f/∂y) |
∞ |
Infinity | Unbounded limit | lim_{x→∞} 1/x = 0 |
≈ |
Approximate equality | Values are close but not exactly equal | π ≈ 3.14 |
x, y, z) usually denote variables; upper‑case (A, B, C) often denote sets, matrices, or constants.