Math Symbol Glossary (A–Z Index)
An alphabetical reference catalog of math symbols across all branches of mathematical study. Search definitions, inspect code points, and copy glyphs directly into your documents.
| Action | Symbol | Name / Term | Branch | Meaning & Definition | LaTeX | Unicode |
|---|---|---|---|---|---|---|
| |x| | Absolute Value / Modulus | Arithmetic Symbols | Distance of a real number from zero regardless of sign. | |x| | U+007C | |
| ℵ₀ | Aleph-Null (Aleph-Nought) | Miscellaneous Math Symbols | Cardinality of the countably infinite set of natural numbers |ℕ|. | \aleph_0 | U+2135 U+2080 | |
| ℵ₁ | Aleph-One | Miscellaneous Math Symbols | The next strictly larger cardinal number after aleph-null. | \aleph_1 | U+2135 U+2081 | |
| α | Alpha (Lowercase) | Greek Math Symbols | Commonly represents angles, significance levels in statistics, or thermal diffusivity. | \alpha | U+03B1 | |
| H₁ | Alternative Hypothesis | Statistics Symbols | The alternative claim accepted when the null hypothesis is rejected. | H_1 \text{ or } H_a | U+0048 U+2081 | |
| ∠ | Angle | Geometry Symbols | Denotes a geometric angle formed by two rays sharing a common vertex. | \angle | U+2220 | |
| Å | Angstrom | Miscellaneous Math Symbols | Unit of length equal to 10⁻¹⁰ meters (0.1 nanometers). | \AA \text{ or } \text{Å} | U+00C5 | |
| ≈ | Approximately Equal To | Comparison Symbols | Indicates that two quantities are nearly equal or rounded. | \approx | U+2248 | |
| ⌒ | Arc | Geometry Symbols | A segment of a curve or perimeter of a circle. | \frown | U+2312 | |
| ∵ | Because / Since | Logic Symbols | Introduces a reason or justification for a stated mathematical deduction. | \because | U+2235 | |
| β | Beta (Lowercase) | Greek Math Symbols | Represents angles, Type II error rates, regression coefficients, or beta function. | \beta | U+03B2 | |
| ⌈x⌉ | Ceiling Function | Algebra Symbols | Smallest integer greater than or equal to x. | \lceil x \rceil | U+2308 U+2309 | |
| χ² | Chi-Square | Statistics Symbols | Test statistic used for tests of independence and goodness of fit. | \chi^2 | U+03C7 U+00B2 | |
| ⊙ | Circled Dot Operator | Algebra Symbols | Hadamard entrywise matrix product or solar mass constant. | \odot | U+2299 | |
| ⊕ | Circled Plus / Direct Sum | Algebra Symbols | Direct sum of modules/vector spaces or exclusive OR (XOR) logic. | \oplus | U+2295 | |
| ⊗ | Circled Times / Tensor Product | Algebra Symbols | Tensor product of vector spaces, modules, or state vectors. | \otimes | U+2297 | |
| ℂ | Complex Numbers | Number Symbols | Set of numbers of the form a + bi, where a, b ∈ ℝ and i = √−1. | \mathbb{C} | U+2102 | |
| P(A|B) | Conditional Probability | Probability Symbols | Probability of event A occurring given that event B has already occurred. | P(A \mid B) | U+2223 | |
| ≅ | Congruent To | Geometry Symbols | Geometric figures having identical size and shape. | \cong | U+2245 | |
| ∮ | Contour Integral (Closed Loop) | Calculus Symbols | Line integral taken along a closed path or contour in complex analysis / physics. | \oint | U+222E | |
| Cov(X,Y) | Covariance | Probability Symbols | Joint variability of two random variables X and Y. | \operatorname{Cov}(X,Y) | U+0043 | |
| ∛ | Cube Root | Arithmetic Symbols | The number that, when raised to the 3rd power, yields the given number. | \sqrt[3]{x} | U+221B | |
| ≔ | Defined As (Colon Equals) | Comparison Symbols | Defines the quantity on the left as being equal to the formula on the right. | \coloneqq \text{ or } := | U+2254 | |
| ° | Degree Sign | Geometry Symbols | A unit of angular measurement equal to 1/360 of a complete circle. | ^\circ | U+00B0 | |
| δ | Delta (Lowercase) | Greek Math Symbols | Epsilon-delta limit proofs, Kronecker delta, or Dirac delta distribution. | \delta | U+03B4 | |
| Δ | Delta (Uppercase) | Greek Math Symbols | Represents change/difference (Δx) or the polynomial discriminant (b² − 4ac). | \Delta | U+0394 | |
| d/dx | Derivative Operator | Calculus Symbols | Instantaneous rate of change of a function with respect to variable x. | \frac{d}{dx} | U+0064 | |
| det(A) | Determinant | Algebra Symbols | A scalar value computed from the elements of a square matrix. | \det(A) \text{ or } |A| | U+0064 | |
| ∼ | Distributed As (∼) | Probability Symbols | Indicates that random variable X follows distribution D (e.g., X ∼ N(μ, σ²)). | \sim | U+223C | |
| ÷ | Division Sign (Obelus) | Arithmetic Symbols | Represents the mathematical division operation. | \div | U+00F7 | |
| ⊭ | Does Not Entail | Logic Symbols | Indicates that A does not semantically entail proposition B. | \nvDash | U+22AD | |
| ⊬ | Does Not Prove | Logic Symbols | Indicates that B cannot be derived from A in this system. | \nvdash | U+22AC | |
| ∬ | Double Integral | Calculus Symbols | Integration over a two-dimensional planar region. | \iint | U+222C | |
| ⊨ | Double Turnstile (Models / Semantic Entailment) | Logic Symbols | Semantic entailment: whenever premises are true, conclusion is guaranteed true. | \vDash | U+22A8 | |
| ∈ | Element Of (Membership) | Set Theory Symbols | Specifies that an object or element belongs to a given set. | \in | U+2208 | |
| ∅ | Empty Set (Null Set) | Set Theory Symbols | The unique set containing zero elements. | \emptyset \text{ or } \varnothing | U+2205 | |
| ε | Epsilon | Greek Math Symbols | Arbitrarily small positive quantity in calculus limits; error term in statistics. | \varepsilon \text{ or } \epsilon | U+03B5 | |
| = | Equals Sign | Comparison Symbols | Equality: expressions on both sides have precisely identical mathematical value. | = | U+003D | |
| e | Euler's Number (e) | Number Symbols | Base of natural logarithms, mathematical constant ≈ 2.718281828... | e | U+0065 | |
| ∃ | Existential Quantifier (There Exists) | Logic Symbols | States that there is at least one element in the domain satisfying the statement. | \exists | U+2203 | |
| E(X) | Expected Value | Probability Symbols | Long-run average value of repetitions of the random variable X. | \mathbb{E}[X] \text{ or } E(X) | U+0045 | |
| ! | Factorial | Arithmetic Symbols | Product of all positive integers less than or equal to n. | n! | U+0021 | |
| ⌊x⌋ | Floor Function | Algebra Symbols | Greatest integer less than or equal to x. | \lfloor x \rfloor | U+230A U+230B | |
| ∜ | Fourth Root | Arithmetic Symbols | Principal fourth root of a number, satisfying r⁴ = x. | \sqrt[4]{x} | U+221C | |
| ∘ | Function Composition | Algebra Symbols | Applies one function to the results of another function. | \circ | U+2218 | |
| f(x) | Function Notation | Algebra Symbols | Represents an output value dependent on the input variable x. | f(x) | U+0066 | |
| γ | Gamma (Lowercase) | Greek Math Symbols | Euler-Mascheroni constant (0.5772...) or photon/gamma ratio in physics. | \gamma | U+03B3 | |
| Γ | Gamma (Uppercase) | Greek Math Symbols | The Gamma function extending factorial to complex numbers: Γ(n) = (n−1)!. | \Gamma | U+0393 | |
| φ | Golden Ratio (Phi) | Number Symbols | Golden ratio constant equal to (1 + √5) / 2 ≈ 1.6180339887... | \phi \text{ or } \varphi | U+03C6 | |
| > | Greater Than | Comparison Symbols | Strict inequality: left value is strictly larger than right value. | > | U+003E | |
| ≥ | Greater Than or Equal To | Comparison Symbols | Non-strict inequality: left value is greater than or equal to right value. | \ge \text{ or } \geq | U+2265 | |
| ∎ | Halmos / End of Proof (Q.E.D.) | Miscellaneous Math Symbols | Tombstone symbol marking the completion of a mathematical theorem proof. | \blacksquare \text{ or } \qed | U+220E | |
| ≡ | Identical To / Congruence | Comparison Symbols | Identical identity for all variables, or modular arithmetic congruence. | \equiv | U+2261 | |
| i | Imaginary Unit | Number Symbols | Unit imaginary number satisfying i² = −1. | i | U+0069 | |
| ∞ | Infinity | Number Symbols | Concept representing boundless, unbounded quantity larger than any real number. | \infty | U+221E | |
| ℤ | Integers (Zahlen) | Number Symbols | Set of all whole numbers: positive, negative, and zero {..., −2, −1, 0, 1, 2, ...}. | \mathbb{Z} | U+2124 | |
| ∫ | Integral | Calculus Symbols | Calculates the area under a curve, antiderivative, or continuous accumulation. | \int | U+222B | |
| ∩ | Intersection | Set Theory Symbols | Set containing only elements common to both sets. | \cap | U+2229 | |
| f⁻¹ | Inverse Function | Algebra Symbols | Reverses the mapping performed by the function f. | f^{-1}(x) | U+0066 U+207B U+00B9 | |
| λ | Lambda (Lowercase) | Greek Math Symbols | Eigenvalues in linear algebra, Poisson rate parameter, or wavelength in physics. | \lambda | U+03BB | |
| ⌈ | Left Ceiling | Algebra Symbols | Rounds a real number up to the nearest integer. | \lceil | U+2308 | |
| ⌊ | Left Floor | Algebra Symbols | Rounds a real number down to the nearest integer. | \lfloor | U+230A | |
| < | Less Than | Comparison Symbols | Strict inequality: left value is strictly smaller than right value. | < | U+003C | |
| ≤ | Less Than or Equal To | Comparison Symbols | Non-strict inequality: left value is smaller than or equal to right value. | \le \text{ or } \leq | U+2264 | |
| lim | Limit | Calculus Symbols | Value that a function or sequence approaches as the input approaches some value. | \lim_{x \to a} | U+006C | |
| ∧ | Logical Conjunction (AND) | Logic Symbols | True if and only if both operands are true. | \land \text{ or } \wedge | U+2227 | |
| ∨ | Logical Disjunction (OR) | Logic Symbols | True if at least one operand is true. | \lor \text{ or } \vee | U+2228 | |
| ⇔ | Logical Equivalence (If and Only If) | Logic Symbols | Bi-conditional: P and Q always share identical truth values. | \iff \text{ or } \Leftrightarrow | U+21D4 | |
| ¬ | Logical Negation (NOT) | Logic Symbols | Inverts the truth value of a proposition. | \neg \text{ or } \lnot | U+00AC | |
| ⇒ | Material Implication (If-Then) | Logic Symbols | Asserts that if premise P is true, then conclusion Q must be true. | \implies \text{ or } \Rightarrow | U+21D2 | |
| ∡ | Measured Angle | Geometry Symbols | Refers specifically to the numerical measure or arc of an angle. | \measuredangle | U+2221 | |
| ℧ | Mho (Inverted Ohm) | Miscellaneous Math Symbols | Unit of electrical conductance (Siemens), upside-down capital Omega. | \mho | U+2127 | |
| − | Minus / Subtraction | Arithmetic Symbols | Denotes subtraction of values or signifies a negative number. | - | U+2212 | |
| ∓ | Minus-Plus Sign | Arithmetic Symbols | Paired with plus-minus sign to indicate opposing branch sign. | \mp | U+2213 | |
| μ | Mu (Lowercase) | Greek Math Symbols | Population mean in statistics, micro (10⁻⁶) prefix, or measure in measure theory. | \mu | U+03BC | |
| ≫ | Much Greater Than | Comparison Symbols | Order of magnitude comparison: left value dominates right value. | \gg | U+226B | |
| ≪ | Much Less Than | Comparison Symbols | Order of magnitude comparison: left value is negligible relative to right value. | \ll | U+226A | |
| × | Multiplication Sign | Arithmetic Symbols | Multiplication of two numbers or cross product of two vectors. | \times | U+00D7 | |
| ∇ | Nabla / Del (Gradient) | Calculus Symbols | Vector differential operator representing gradient, divergence, or curl. | \nabla | U+2207 | |
| ℕ | Natural Numbers | Number Symbols | Set of positive counting integers: {1, 2, 3, 4, ...} (or {0, 1, 2, ...}). | \mathbb{N} | U+2115 | |
| ⊄ | Not a Subset | Set Theory Symbols | First set contains at least one element not present in the second set. | \not\subset | U+2284 | |
| ≉ | Not Almost Equal To | Comparison Symbols | Indicates that two values are not approximately equal. | \not\approx | U+2249 | |
| ∉ | Not an Element Of | Set Theory Symbols | Indicates that an element does NOT belong to a set. | \notin | U+2209 | |
| ≠ | Not Equal To | Comparison Symbols | Inequality: indicates that two expressions have distinct, non-matching values. | \neq \text{ or } \ne | U+2260 | |
| ≢ | Not Identical To | Comparison Symbols | Two functions or modular equations are not identically equal. | \not\equiv | U+2262 | |
| ∦ | Not Parallel | Geometry Symbols | Indicates that two lines or vectors are not parallel. | \nparallel | U+2226 | |
| H₀ | Null Hypothesis | Statistics Symbols | Default baseline assumption tested in statistical hypothesis testing (no effect/no difference). | H_0 | U+0048 U+2080 | |
| ω | Omega (Lowercase) | Greek Math Symbols | Angular frequency in physics, first infinite ordinal in set theory. | \omega | U+03C9 | |
| Ω | Omega (Uppercase) | Greek Math Symbols | Sample space in probability; Ohm resistance in physics; asymptotic lower bound in computer science. | \Omega | U+03A9 | |
| p | p-Value | Statistics Symbols | Probability of obtaining results at least as extreme as observed data under H₀. | p | U+0070 | |
| ∥ | Parallel | Geometry Symbols | Indicates that two lines or planes lie in the same plane and never intersect. | \parallel | U+2225 | |
| ∂ | Partial Derivative (Del / Curly d) | Calculus Symbols | Derivative of a multivariable function with respect to one variable holding others constant. | \partial | U+2202 | |
| r | Pearson Correlation Coefficient | Statistics Symbols | Linear correlation between two variables, ranging from −1 to +1. | r | U+0072 | |
| ‰ | Per Mille (Permil) | Arithmetic Symbols | Per thousand; parts per 1,000. | \textperthousand | U+2030 | |
| % | Percent | Arithmetic Symbols | Per hundred; parts per 100. | \% | U+0025 | |
| ⊥ | Perpendicular | Geometry Symbols | Indicates that two lines, rays, or vectors intersect at right angles (90°). | \perp | U+22A5 | |
| π | Pi (Lowercase) | Greek Math Symbols | Mathematical constant equal to the ratio of a circle's circumference to diameter (≈ 3.14159). | \pi | U+03C0 | |
| + | Plus / Addition | Arithmetic Symbols | Denotes addition of two values or signifies a positive number. | + | U+002B | |
| ± | Plus-Minus Sign | Arithmetic Symbols | Specifies confidence intervals, measurement tolerances, or two roots (positive and negative). | \pm | U+00B1 | |
| ℘(A) | Power Set | Set Theory Symbols | Set of all subsets of A, including the empty set and A itself. | \mathcal{P}(A) | U+2118 | |
| f'(x) | Prime Derivative Notation | Calculus Symbols | Lagrange's notation for the first derivative of a function. | f'(x) | U+2032 | |
| ℙ | Prime Numbers Set | Number Symbols | Set of natural numbers greater than 1 having exactly two factors (1 and itself). | \mathbb{P} | U+2119 | |
| P(A) | Probability of Event A | Probability Symbols | The likelihood of event A occurring, ranging between 0 and 1 inclusive. | P(A) \text{ or } \mathbb{P}(A) | U+0050 | |
| ∏ | Product Operator (Capital Pi) | Algebra Symbols | Iterative multiplication of a sequence of factors over a specified range. | \prod_{i=1}^n | U+220F | |
| ⊂ | Proper Subset Of | Set Theory Symbols | Set A is contained in set B, and A is not strictly equal to B. | \subset | U+2282 | |
| ⊃ | Proper Superset | Set Theory Symbols | Strictly contains all elements of the second set with at least one more. | \supset | U+2283 | |
| ∝ | Proportional To | Algebra Symbols | Indicates that two quantities vary in constant ratio. | \propto | U+221D | |
| ⨌ | Quadruple Integral | Calculus Symbols | Integral evaluated across a four-dimensional mathematical volume. | \iiiint | U+2A0C | |
| ℚ | Rational Numbers (Quotients) | Number Symbols | Set of numbers expressible as a fraction a/b where a, b ∈ ℤ and b ≠ 0. | \mathbb{Q} | U+211A | |
| → | Ray / Vector Arrow | Geometry Symbols | Denotes a directed vector or geometric ray extending indefinitely in one direction. | \vec{v} \text{ or } \to | U+2192 | |
| ℝ | Real Numbers | Number Symbols | Set of all points on the continuous number line, including rationals and irrationals. | \mathbb{R} | U+211D | |
| ℏ | Reduced Planck Constant (H-bar) | Miscellaneous Math Symbols | Planck constant divided by 2π (h / 2π). | \hbar | U+210F | |
| ⌉ | Right Ceiling | Algebra Symbols | Closing delimiter for the ceiling rounding function. | \rceil | U+2309 | |
| ⌋ | Right Floor | Algebra Symbols | Closing delimiter for the floor rounding function. | \rfloor | U+230B | |
| x̄ | Sample Mean (X-Bar) | Statistics Symbols | Arithmetic average of data points in a sample. | \bar{x} | U+0078 U+0304 | |
| s | Sample Standard Deviation | Statistics Symbols | Standard deviation computed across sample observations with n−1 denominator. | s | U+0073 | |
| s² | Sample Variance | Statistics Symbols | Unbiased estimate of population variance from sample data. | s^2 | U+0073 U+00B2 | |
| |A| | Set Cardinality | Set Theory Symbols | Number of elements in set A. | |A| \text{ or } \#A | U+007C | |
| \ | Set Difference (Relative Complement) | Set Theory Symbols | Elements present in set A that are not in set B. | \setminus | U+2216 | |
| σ | Sigma (Lowercase) | Greek Math Symbols | Population standard deviation in statistics; stress in mechanical physics. | \sigma | U+03C3 | |
| Σ | Sigma (Uppercase) | Greek Math Symbols | Summation notation over indices; covariance matrix in multivariable statistics. | \Sigma | U+03A3 | |
| ∼ | Similar To | Geometry Symbols | Geometric figures having identical shapes and proportional corresponding sides. | \sim | U+223C | |
| √ | Square Root (Radical) | Arithmetic Symbols | Yields the principal non-negative value that, when squared, equals the radicand. | \sqrt{x} | U+221A | |
| ⊆ | Subset Of or Equal To | Set Theory Symbols | Every element of set A is also in set B (A may equal B). | \subseteq | U+2286 | |
| ∑ | Summation (Sigma) | Algebra Symbols | Iterative summation of a sequence of terms indexed over a specified range. | \sum_{i=1}^n | U+2211 | |
| ⊇ | Superset of or Equal To | Set Theory Symbols | Contains all elements of the second set, or is identical. | \supseteq | U+2287 | |
| ∯ | Surface Integral | Calculus Symbols | Closed double integral over a closed 2D boundary surface. | \oiint | U+222F | |
| τ | Tau (Circle Constant) | Greek Math Symbols | Circle constant equal to 2π ≈ 6.28318 radians in a full turn. | \tau | U+03C4 | |
| ∄ | There Does Not Exist | Logic Symbols | No member of the specified domain satisfies the given condition. | \nexists | U+2204 | |
| ∴ | Therefore | Logic Symbols | Used before a logical conclusion derived from preceding premises. | \therefore | U+2234 | |
| θ | Theta (Lowercase) | Greek Math Symbols | Standard notation for angles in trigonometry, polar coordinates, and parametric curves. | \theta | U+03B8 | |
| △ | Triangle | Geometry Symbols | Denotes a geometric triangle polygon with 3 sides and 3 vertices. | \triangle | U+25B3 | |
| ∭ | Triple Integral | Calculus Symbols | Integration over a three-dimensional solid volume. | \iiint | U+222D | |
| ⊢ | Turnstile (Proves / Entails) | Logic Symbols | Syntactic deduction: conclusion can be formally proved from assumptions. | \vdash | U+22A2 | |
| ∪ | Union | Set Theory Symbols | Combines all elements that belong to set A, set B, or both. | \cup | U+222A | |
| ∀ | Universal Quantifier (For All) | Logic Symbols | Indicates that the predicate statement holds for all members of a domain. | \forall | U+2200 | |
| Var(X) | Variance | Probability Symbols | Measure of the dispersion of a random variable from its mean: E[(X − E[X])²]. | \operatorname{Var}(X) | U+0056 | |
| ‖x‖ | Vector Norm / Double Bar | Algebra Symbols | Length or magnitude of a vector in a normed vector space. | \|x\| | U+2016 | |
| ∰ | Volume Integral | Calculus Symbols | Closed triple integral over a 3D closed hypersurface. | \oiiint | U+2230 | |
| ℘ | Weierstrass p | Miscellaneous Math Symbols | Weierstrass elliptic function or power set indicator. | \wp | U+2118 |
Glossary FAQ
How is this mathematical symbol glossary organized?
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How are character definitions verified?
Every term and code point is checked against official ISO 80000-2:2019 specifications, Unicode Technical Report #25, and AMS-LaTeX mathematical notation conventions.