# 2. The Concept of a Function

1. Ulrich L. Rohde1,2,
2. G. C. Jain3,
3. Ajay K. Poddar2 and
4. A. K. Ghosh4

Published Online: 28 DEC 2011

DOI: 10.1002/9781118130155.ch2

## Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners

#### How to Cite

Rohde, U. L., Jain, G. C., Poddar, A. K. and Ghosh, A. K. (2011) The Concept of a Function, in Introduction to Differential Calculus: Systematic Studies with Engineering Applications for Beginners, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118130155.ch2

#### Author Information

1. 1

BTU Cottbus, Germany

2. 2

Synergy Microwave Corporation, Paterson, NJ, USA

3. 3

Defense Research & Development Organization, Maharashtra, India

4. 4

Department of Aerospace Engineering, Indian Institute of Technology – Kanpur, Kanpur, India

#### Publication History

1. Published Online: 28 DEC 2011
2. Published Print: 9 DEC 2011

#### ISBN Information

Print ISBN: 9781118117750

Online ISBN: 9781118130155

## SEARCH

### Keywords:

• “function,” as language of sets, modes of expression;
• function, and domain, codomain, image, range;
• infinity and algebra of infinity

### Summary

This chapter contains sections titled:

• Introduction

• Equality of Ordered Pairs

• Relations and Functions

• Definition

• Domain, Codomain, Image, and Range of a Function

• Distinction Between “f” and “f(x)”

• Dependent and Independent Variables

• Functions at a Glance

• Modes of Expressing a Function

• Types of Functions

• Inverse Function f−1

• Comparing Sets without Counting their Elements

• The Cardinal Number of a Set

• Equivalent Sets (Definition)

• Finite Set (Definition)

• Infinite Set (Definition)

• Countable and Uncountable Sets

• Cardinality of Countable and Uncountable Sets

• Second Definition of an Infinity Set

• The Notion of Infinity

• An Important Note About the Size of Infinity

• Algebra of Infinity (∞)