Mathematical Notions And Terminology

Mathematical Notions And Terminology

Mathematical Notions And Terminology


As in any mathematical subject , we begin with a discussion of the basic mathematical objects, tools, and notation that we expect to use.


A set is a group of objects represented as a unit. Sets may contain any type of object, including numbers, symbols, and even other sets.

  • The objects in a set are called its elements or members.
  • For sets, we use a type of picture called a Venn diagram
  • The set with 0 members is called the empty set


A sequence of objects is a list of these objects in some order. As with sets, sequences may be finite or infinite. Finite sequences often are called tuples

  • We usually designate a sequence by writing the list within parentheses.
  • In a set, the order doesn’t matter, but in a sequence it does
  • Repetition does matter in a sequence, but it does not matter in a set


A function is an object that sets up input-output relationship. A function takes an input and produces an output.

  • A function is called a mapping if f(a) = b, we say that f maps a to b.
  • The set of possible inputs to the function is called its domain.
  • The outputs of a function come from a set called its range.
  • The notation for saying that f is a function with domain D and range R is f : D –> R
  • A function may not necessarily use all the elements of the specified range.
  • A function that does use all the elements of the range is said to be onto the range.


An undirected graph, or simply a graph, is a set of points with lines connecting some of the points.

  • The points are called nodes or vertices, and the lines are called edges.
  • The number of edges at a particular node is the degree of that node.
  • Graphs frequently are used to represent data.
  • A path in a graph is a sequence of nodes connected by edges.
  • A simple path is a path that doesn’t repeat any nodes.
  • A graph is connected if every two nodes have a path between them.
  • A path is a cycle if it starts and ends in the same node.
  • A simple cycle is one that contains at least three nodes and repeats only the first and last nodes.
  • A graph is a tree if it is connected and hs no simple cycles

Mathematical Notions And Terminology Summary

Alphabet A finite set of objects called symbols
Argument An input to a function
Binary operation A relation whose domain is a set of pairs
Cartesian product An operation on sets forming a set of all tuples of elements from respective sets
Cycle A path that starts and ends in the same node
Domain The set of possible inputs to a function
Edge A line in a graph
Element An object in a set
Empty String The string of length zero
Function An operation that translates inputs inot outputs
Graph A collection of points and lines connecting some pairs of points
Language A set of strings
Member An object in a graph
Node A point in a graph
Pair A list of two elements, also called a 2-tuple
Path A sequence of nodes in a graph connected by edges
Property A predicate
Predicate A function whose range is { TRUE, FALSE }
Range The set from which outputs of a function are drawn
Vertex A point in a graph

Leave a Comment

Your email address will not be published. Required fields are marked *

PYQ of History UGC NET UGC NET Mathematical Reasoning and Aptitude ICT (Digital Initiatives) | UGC NET | paper – 1 The Scope of Information and Communication Technology(ICT) PYQ of People, Development, and Environment Top 30 PYQ of HINDI | UGC NET – 2023 Top 30 PYQ of Teaching Aptitude PYQ of Research Aptitude | NTA UGC NET | Paper 1 | Part 1 UGC NET Paper 1 Syllabus | Updated | 2023 Types of Research | Research Aptitude | nta ugc net | UGC NET 2023