Math Symbols
The following is a glossary of mathematical symbols. This list assists in understanding discrete mathematics and related software engineering concepts.
Basic Operations
| Symbol | Name | Description |
|---|
| $+$ | Addition | Sums two values. |
| $-$ | Subtraction | Subtracts one value from another. |
| $\times$ | Multiplication | Multiplies two values. |
| $\div$ | Division | Divides one value by another. |
| $\sqrt{x}$ | Square Root | Returns the principal square root of a number. |
Set Theory
| Symbol | Name | Description | Example |
|---|
| $\emptyset$ | Empty Set | A set containing no elements. | $A = \emptyset$ |
| $\cup$ | Union | Combines all elements from two sets. | $A \cup B$ |
| $\cap$ | Intersection | Identifies elements common to both sets. | $A \cap B$ |
| $\setminus$ | Difference | Removes elements of the second set from the first. | $A \setminus B$ |
| $\Delta$ | Symmetric Difference | Combines elements in either set, but not in both. | $A \Delta B$ |
| $\in$ | Set Membership | Indicates an element belongs to a set. | $x \in A$ |
| $\notin$ | Non-Membership | Indicates an element does not belong to a set. | $x \notin A$ |
| $\subseteq$ | Subset | A set where all elements exist in another set. | $A \subseteq B$ |
| $\subset$ | Proper Subset | A subset that is not equal to the superset. | $A \subset B$ |
Basic Logic
| Symbol | Name | Description | Example |
|---|
| $\neg$ | Negation | Logical NOT. Reverses the truth value of a statement. | $\neg P$ |
| $\land$ | Conjunction | Logical AND. True if both statements are true. | $P \land Q$ |
| $\lor$ | Disjunction | Logical OR. True if at least one statement is true. | $P \lor Q$ |
| $\implies$ | Implication | Conditional statement ("If $P$, then $Q$"). | $P \implies Q$ |
| $\iff$ | Biconditional | Equivalence ("$P$ if and only if $Q$"). | $P \iff Q$ |
| $\equiv$ | Equivalence | Denotes identical logical statements. | $P \equiv Q$ |
| $\exists$ | Existential Quantifier | "There exists..." at least one element satisfying the condition. | $\exists x$ |
| $\forall$ | Universal Quantifier | "For all..." elements, the condition is true. | $\forall x$ |
| $\exists!$ | Uniqueness | "There exists exactly one" element satisfying the condition. | $\exists! x$ |
Number Sets (Blackboard Bold)
Blackboard bold font denotes standard mathematical number sets.
| Symbol | Name | Description |
|---|
| $\mathbb{N}$ | Natural Numbers | Counting numbers ($0, 1, 2, 3, \dots$). |
| $\mathbb{Z}$ | Integers | Whole numbers, including negatives. |
| $\mathbb{Q}$ | Rational Numbers | Numbers expressible as a fraction of two integers. |
| $\mathbb{R}$ | Real Numbers | All rational and irrational numbers. |
| $\mathbb{C}$ | Complex Numbers | Numbers with real and imaginary parts ($a + bi$). |
Greek Letters
Greek letters appear in mathematics to represent variables, constants, and functions. The table lists uppercase, lowercase, and variant forms.
| Name | Uppercase | Lowercase | Variant |
|---|
| Alpha | $A$ | $\alpha$ | |
| Beta | $B$ | $\beta$ | |
| Gamma | $\Gamma$ | $\gamma$ | |
| Delta | $\Delta$ | $\delta$ | |
| Epsilon | $E$ | $\epsilon$ | $\varepsilon$ |
| Zeta | $Z$ | $\zeta$ | |
| Eta | $H$ | $\eta$ | |
| Theta | $\Theta$ | $\theta$ | $\vartheta$ |
| Iota | $I$ | $\iota$ | |
| Kappa | $K$ | $\kappa$ | $\varkappa$ |
| Lambda | $\Lambda$ | $\lambda$ | |
| Mu | $M$ | $\mu$ | |
| Nu | $N$ | $\nu$ | |
| Xi | $\Xi$ | $\xi$ | |
| Omicron | $O$ | $o$ | |
| Pi | $\Pi$ | $\pi$ | $\varpi$ |
| Rho | $P$ | $\rho$ | $\varrho$ |
| Sigma | $\Sigma$ | $\sigma$ | $\varsigma$ |
| Tau | $T$ | $\tau$ | |
| Upsilon | $\Upsilon$ | $\upsilon$ | |
| Phi | $\Phi$ | $\phi$ | $\varphi$ |
| Chi | $X$ | $\chi$ | |
| Psi | $\Psi$ | $\psi$ | |
| Omega | $\Omega$ | $\omega$ | |