This page is a compact cheat sheet of common mathematical operators, grouped by category. Each entry lists symbols, meaning, a quick example, and (when relevant) programming equivalents.
1) Arithmetic
| Operator | Symbols | Meaning | Example | Programming equivalents / notes |
|---|---|---|---|---|
| Addition | + | Add two numbers | 4 + 5 = 9 | + |
| Subtraction | − | Subtract second from first | 9 − 5 = 4 | - (ASCII minus) |
| Multiplication | ×, ·, * | Multiply | 3 × 5 = 15 | * |
| Division | ÷, / | Divide | 12 ÷ 3 = 4 | / (integer vs. floating matters) |
| Exponentiation | ^, superscript | Power | b^n | ** (Python), Math.pow(b,n) |
| Roots | √, ⁿ√ | Square/nth root | √9 = 3, ³√8 = 2 | sqrt(x) |
| Factorial | ! | Product 1 to n | 5! = 120 | factorial(n) |
| Percentage | % | Parts per hundred | 50% = 50/100 | Beware % = modulo in code |
| Modulo | mod, % | Remainder | 7 mod 3 = 1 | % (C/Java/JS/Python) |
2) Equality & Inequality
| Operator | Symbols | Meaning | Example | Notes |
|---|---|---|---|---|
| Equality | = | Same value | 2 + 2 = 4 | In code: == (equality), === (strict) |
| Not equal | ≠ | Different values | π ≠ 3 | !=, <> (SQL) |
| Less / Greater | <, > | Comparison | 2 < 3, 5 > 4 | |
| Less-or-equal | ≤ | ≤ | x ≤ 10 | <= |
| Greater-or-equal | ≥ | ≥ | y ≥ 0 | >= |
3) Unary & Absolute / Rounding
| Operator | Symbols | Meaning | Example | Notes |
|---|---|---|---|---|
| Unary plus | +x | Leave unchanged | +7 = 7 | |
| Unary minus | −x | Negation | −(−3) = 3 | |
| Absolute value | |x| | Magnitude | |−5| = 5 | abs(x) |
| Floor | ⌊x⌋ | Round down | ⌊2.9⌋ = 2 | floor(x) |
| Ceiling | ⌈x⌉ | Round up | ⌈2.1⌉ = 3 | ceil(x) |
| Sign | sgn(x) | −1, 0, 1 | sgn(−2)=−1 | sign(x) |
4) Summation, Product, Calculus
| Operator | Symbols | Meaning | Example | Notes |
|---|---|---|---|---|
| Summation | ∑ | Sum over index | ∑_{i=1}^n i | Sigma notation |
| Product | ∏ | Product over index | ∏_{k=1}^n k = n! | Pi notation |
| Derivative | d/dx, ' | Rate of change | d/dx(x^2)=2x | Higher order: d²/dx² |
| Integral | ∫ | Accumulated area | ∫_0^1 x dx = 1/2 | Definite/indefinite |
| Limit | lim | Approach a value | lim_{x→0} sin x / x = 1 | |
| Difference | Δ | Discrete change | Δy = y_{n+1}-y_n | |
| Nabla | ∇ | Grad/Div/Curl | ∇f, ∇·F, ∇×F | Vector calculus |
5) Linear Algebra & Vector Ops
| Operator | Symbols | Meaning | Example | Notes |
|---|---|---|---|---|
| Dot product | · | Scalar from vectors | a·b = |a||b|cosθ | dot(a,b) |
| Cross product | × | Vector orthogonal | a×b | 3-D only |
| Transpose | T | Flip rows/cols | A^T | |
| Determinant | det(A) | Volume scale | det([[a,b],[c,d]])=ad−bc | |
| Matrix multiply | AB | Linear comp. | A(BC)=(AB)C | @ (Python), * (NumPy) |
6) Logic
| Operator | Symbols | Meaning | Example | Programming equivalents |
|---|---|---|---|---|
| NOT | ¬, ! | Negation | ¬P | !P, not P |
| AND | ∧ | Conjunction | P ∧ Q | &&, and |
| OR | ∨ | Disjunction | P ∨ Q | ||, or |
| Implication | → | If…then | P → Q | (!P) or Q (material) |
| Equivalence | ↔ | Iff | P ↔ Q | (P→Q)∧(Q→P) |
7) Sets
| Operator | Symbols | Meaning | Example | Notes |
|---|---|---|---|---|
| Element of | ∈, ∉ | Membership | 2 ∈ ℕ, −1 ∉ ℕ | |
| Subset / Superset | ⊆, ⊇ | Inclusion | {1,2} ⊆ ℕ | Proper: ⊂, ⊃ |
| Union | ∪ | Combine | {1}∪{2}={1,2} | |
| Intersection | ∩ | Common | {1,2}∩{2,3}={2} | |
| Set difference | ∖ | A without B | {1,2,3}∖{2}={1,3} | |
| Complement | Aᶜ | Outside A | U∖A | Needs universe U |
8) Functions & Specials
| Operator | Symbols | Meaning | Example | Notes |
|---|---|---|---|---|
| Reciprocal | 1/x | Multiplicative inverse | 1/4 = 0.25 | |
| Mean | μ, \bar{x} | Average | μ = (1/n)∑x_i | |
| Median | med(x) | Middle value | ||
| Variance | σ², Var | Spread of data | σ² = E[(X−μ)²] | |
| Square / Cube | x², x³ | Power 2 / 3 | 3²=9, 2³=8 | |
| Exponential | exp(x) | e^x | exp(0)=1 | |
| Logarithm | log, ln, log₁₀, log₂ | Inverse of exp | ln(e)=1 | Base matters |
| Clamp / Clip | min/max | Limit range | min(max(x,a),b) |
Quick Notes & Conventions
- Symbols vs. ASCIIMany symbols (e.g.,
−,×,÷,≤) have ASCII fallbacks (-,*,/,<=). Be consistent within a document or codebase. - Operator precedence (informal)factorial/parentheses, exponents, unary ±, multiply/divide/mod, add/subtract, comparisons, logic.
- Programming modulo
%is remainder; some languages differ on negative operands. - Logarithmsdefault base may vary (
lnfor natural;log10orlogin calculators). Always specify base in technical writing.
Key terms in plain language
Open a term for a concise explanation of language used on this page.
Broadband
A general term for always-on, high-speed Internet access. Broadband can be delivered over fiber, cable, DSL, fixed wireless, cellular, or satellite networks.
Cloud Computing
Computing resources—such as applications, servers, storage, or databases—delivered from remote infrastructure and scaled as requirements change.
Cybersecurity
The practices and controls used to protect identities, devices, networks, applications, and data from unauthorized access, disruption, or manipulation.
Identity and Access Management (IAM)
The systems and policies that determine who a user is, what resources they may access, and how that access is authenticated and reviewed.
API
An application programming interface is a defined way for software systems to exchange data or request functions from one another.
Artificial Intelligence (AI)
Software designed to perform tasks involving prediction, classification, generation, reasoning, or decision support. Business use still requires clear data, governance, security, and human accountability.