# Mathematical Terms

List of Mathematical Terms used in theory of computation

Alphabet – A finite set of objects

Argument – An input to a function

Binary relation – A relation with domain as set of pairs

Boolean operation – Operation on bolean values

Boolean value – TRUE or FALSE (1 or 0)

Cartesian product – An operation on sets forming a set of all tuples of elements from respective sets

Complement – An operation on a set, forming the set of all non-existent elements

Concatenation – Joining of strings of one set with that of another

Conjunction – Boolean AND operation

Connected graph – A graph with paths that connect every two nodes

Cycle – A path that starts and ends in the same node

Directed graph – A collection of points and arrows that connect some pairs of points

Disjunction – Boolean OR operation

Domain – Set of possible inputs to a function

Edge – A line in a graph

Element – An object in a set

Empty set – Set without any member

Empty string – Zero length string

Equivalence relation – A binary relation that is reflective, symmetric and transitive

Function – An operation that converts inputs into outputs

Graph – A collection of points and lines that connect some pairs of points

Intersection – An operation on sets to form a set of common elements

k-tuple – A list of k objects

Language – Set of strings

Member – An element in a set

Node – A point in a graph

Pair – A list of two elements

Path – Sequence of nodes in a graph connected by edges

Predicate – A function whose range is {TRUE, FALSE}

Property – A predicate

Range – The set from which outputs of a function are drawn

Relation – A predicate, most typically when the domain is a set of k-tuples

Sequence – List of objects

Set – Group of objects

Simple path – A path without repetition

String – List of symbols representing alphabets

Symbol – An alphabet

Tree – A connected graph without simple cycles

2-Tuple – List of two elements

Union – An operation on sets to combine the elements into a single set

Vertex – A point in a graph