Math Symbols

The following is a glossary of math symbols. I wrote it as part of my early grad studies in software engineering. It's meant to assist me in understanding discrete mathematics.

The Glossary

The easy ones

Addition: $+$

Subtraction: $-$

Multiplication: $\times$

Division: $\div$

Square Root: $\sqrt{x}$

Set Theory

Empty Set: $\emptyset$

Union: $\cup$ (a union is the result of combining two sets)

Intersection: $\cap$ (an intersection is the result of finding common elements between two sets)

Difference: $\setminus$ (a difference is the result of removing elements from one set that are also in another set, for example $A \setminus B$)

Symmetric Difference: $\Delta$ (a symmetric difference is the result of combining the differences between two sets)

Set Membership: $\in$ (an element is a member of a set, for example $x \in {1, 2, 3}$. Read as "x is an element of the set {1, 2, 3}")

Set Non-Membership: $\notin$ (an element is not a member of a set)

Basic Logic

Negation: $\neg$ (a negation is the opposite of a statement, for example $\neg P$)

Conjunction: $\land$ (a conjunction is the result of combining two statements with "and", for example $P \land Q$)

Disjunction: $\lor$ (a disjunction is the result of combining two statements with "or", for example $P \lor Q$)

Implication: $\implies$ (an implication is the result of combining two statements with "if...then", for example $P \implies Q$)

Biconditional: $\iff$ (a biconditional is the result of combining two statements with "if and only if", for example $P \iff Q$)

Equivalence: $\equiv$ (an equivalence is the result of combining two statements with "is equivalent to", for example $P \equiv Q$)

Existential Qualification: $\exists$ (an existential qualification is the result of combining a statement with "there exists", for example $\exists x \in \mathbb{R}$)

Universal Qualification: $\forall$ (a universal qualification is the result of combining a statement with "for all", for example $\forall x \in \mathbb{R}$)

Uniqueness Qualification: $\exists!$ (a uniqueness qualification is the result of combining a statement with "there exists exactly one", for example $\exists! x \in \mathbb{R}$)

Blackboard Bold

Letters in the "blackboard bold" font are used to denote mathematical sets and numbers.

Natural Numbers: $\mathbb{N}$

Integers: $\mathbb{Z}$

Rational Numbers: $\mathbb{Q}$

Real Numbers: $\mathbb{R}$

Complex Numbers: $\mathbb{C}$