A-Z Popular Blog Coding Search »
Culture
 Advertisements
Related Guides
Computing Culture
Culture Change

Culture Characteristics

American Culture

Cultural Rights

Food Culture

Why Division By Zero is Undefined

 , updated on
Division by zero is division where the denominator is zero such as 1/0. This is always undefined and has no meaning. The following are potential solutions to division by zero designed to illustrate why this is the case.

Infinity Theories

One way to approximate answers for division by zero is to divide by smaller and smaller numbers to get closer to zero to see what happens:
1/0.1 = 10
1/0.0000001 = 10,000,000
1/0.0000000001 = 10,000,000,000
Looking at this you might assume that division by zero equals infinity as answers get larger and larger as the denominator approaches zero.
1/0 = ∞ ????
However, if you approach zero from the other side by using small negative numbers the results are very different:
1/-0.1 = -10
1/-0.0000001 = -10,000,000
1/-0.0000000001 = -10,000,000,000
These results imply that division by zero results in negative infinity as answers get smaller and smaller as the denominator approaches 0.
1/0 = -∞ ????
Therefore, attempting to solve division by zero by approximation yields two equally valid arguments: the answer is infinity and negative infinity. As there are no two numbers further apart than infinity and negative infinity, this indicates the answer is indeterminate and undefined.

A Proof of 1=2

If division by zero is possible, it allows for proofs of things we know not to be true. For example:
Assumptions:
0 × 1 = 0
0 × 2 = 0
By deduction:
0 × 1 = 0 × 2
If division by zero is allowed, this can be simplified:
(0 x 1)/0 = (0 x 2)/0
As multiplication and division are inverse operations the zeros can be canceled out and this can be reduced to:
1 = 2
Therefore, if division by zero is defined, 1=2.

Inverse Operations

Multiplication and division are inverse operations, meaning that they can undo each other. For example:
(2/3) × 3 = 2
(33 / 4) × 4 = 33
(33,000 / 44) × 44 = 33,000
This doesn't work for division by zero:
(1 / 0) × 0 ≠ 1
Any number multiplied by 0 is 0. As such, there is no possible value for (1/0) that can satisfy the principle that multiplication and division are inverse operations.

What About 0/0?

There are two equally valid and conflicting theories for the answer to 0/0:
Zero divided by any number is 0. Therefore, 0/0 = 0
Any number divided by itself is 1. Therefore 0/0 = 1
As these are equally valid theories that contradict, the answer is indeterminate and undefined.

Notes

Division by zero generates an exception on most computing platforms such that it can potentially crash software. As such, division by zero is often handled as a special case in code. Not handling division by zero in some intelligent way is a common type of bug.
Overview: Division By Zero
Type
Definition
Division where the denominator is zero.
Related Concepts

Computing

This is the complete list of articles we have written about computing.
Abstraction
Affective Computing
Algorithms
AI
Big Data
Binary
Blockhead
Brute Force
Caching
Character Set
Client-Server
Coding
Coding Principles
Colocation
Compression
Computing
Cryptographic Keys
Cryptography
Dark Data
Data
Data Centers
Data Infrastructure
Data Integration
Data Migration
Data Processing
Data Science
Data Security
Deep Learning
Deep Magic
Digital
Edge Computing
Edit Distance
Emergence
End-User Computing
Everything Is A File
Files
Gamification
Garbage In, Garbage Out
Halt And Catch Fire
Hello World
Hexadecimal
Horizontal Scale
Instance
Internet Of Things
IT Infrastructure
Job Processing
Key Stretching
Last Mile
Latency
Local Area Network
Meet-me Room
Micro Data Center
Microcomputer
Moore's Law
Near Real-Time
Network Infra
Networking
Networks
Operating Systems
Overlay Network
Peer-to-peer
Precomputation
Private IP
Private Network
Proof Of Work
Proxy Server
Key Cryptography
Qualitative Data
Random Seed
Reluctant Algorithms
Reverse Algorithms
Reverse Proxy
Swarm Intelligence
System on a Chip
Throughput
Unstructured Data
Vertical Scale
Virtual Machine
Yobibyte
If you enjoyed this page, please consider bookmarking Simplicable.
 

Halt And Catch Fire

The meaning of halt and catch fire.

Hello World

Hello World, this is an article about Hello World.

Answer to the Ultimate Question of Life, the Universe, and Everything

An overview of a well known parody of computing.

Garbage In Garbage Out

A definition of garbage in, garbage out with an example.

Information Age

An overview of the information age with examples.

Information Culture

An overview of information culture with examples.

Computing

Examples of computing in everyday life.

Delimited Text File

The common types of delimited text file.

Binary

Binary completely explained.

Hexadecimal

An overview of hexadecimal as it relates to computing.

Application vs Service

The difference between application software and services.

Data Processing

A definition of data processing with examples.

Virtual Machine

The common types of virtual machine.

System on a Chip

A definition of system on a chip with examples.

Embedded System

The definition of embedded system with examples.

Real-Time

A definition of real-time with examples.
The most popular articles on Simplicable in the past day.

New Articles

Recent posts or updates on Simplicable.
Site Map