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# Composition Definition/Meaning:

1. (relative product) A method of combining functions in a serial manner. The composition of two functions

ƒ:x →Y and g :Y → Z

is the function

h : X → Z

with the property that

h(x) = g(ƒ(x))

This is usually written as g o ƒ The process of performing composition is an operation between functions of suitable kinds. It is associative, and identity functions fulfill the role of units.

If R denotes the set of real numbers and

ƒ : R → R,ƒ(x) = sin(x)

g : R → R, g(x) = x2 + 3

then ƒ o g is the function h:

h : R → R, h(x) = sin(x2 + 3)

The idea of composition of functions can be extended to functions of several variables.

2. A subdivision of a positive integer n into parts a1, a2, ... ak in which the ordering is significant and in which

n = a1+ a2 + ... + ak

where each a1 is a positive integer. It is thus similar to a partition but in a partition the ordering is not significant. In general the number of compositions of n is 2n-1.

## Near by Terms:

COBOL or Cobol
Cocktail Shaker Sort
CODASVL
Code
8421Code
Codebook
Codec
Code Length
Coder-Decoder
Codeword, Codeword Length
Coding
Coding Bounds
Coding Standards
Coding Theorems
Coding Theory
Codomain
Collating Sequence
Collator
Collector
Collision, Collision Detection
Color Display
Colossus
Column-Major Order
Column-Ragged
Column Vector
COM
COMAL
Combinational Circuit (combinatorial circuit)
Combinatorial Circuit
Combinatorial
Combinatory Logic
Command
Command Control Program
Command Language
Comment
COMMON Area
Common Carrier
Communication Channel
Communication Network
Communication Processor
Communication Server
Communication Subnetwork (subnet)
Communication System
Communication Theory
Commutative Group (abelian group)
Commutative Law
Commutative Operation
Commutative Ring
Commutative Semiring
Compaction
Comparator
Comparison Counting Sort
Compartmentalization (compartmentation)
Compatibility
Compilation Time
Compiler
Compiler-Compiler
Complement Number System
Complete Graph
Complete Tree
Complexity
Complexity Classes
Complexity Function (work function)
Complexity Measure
Composition
Compression Coding
Computability
Computable (Turing computable)
Computable Function
Computational Psychology
Computer
Computer-Aidd Instruction (CAI)
Computer-Aided Manufacturing (CAM) CAM
Computer-Aided Testing (CAT)
Computer Architecture
Computer-Assisted Instruction (CAI)
Computer-Based Learning (CBL)
Computer Family
Computer Graphics
Computer Logic
Computer Mail
Computer-Managed Instruction (CMl)
Computer Manager
Computer Network
Computer Power
Computer Science
Computer- Services Manager
Computer Word
Concatenated Code
Concatenated Coding Systems
Concatenation
Concatenation Closure
Concentrator
Concurrency
Concurrent Programming
Conditional
Conditional Branch Instruction
Conditional Transfer
Condition Number
Confidence Interval
Configuration
Configuration Management
Configured -in. -off, -out
Confluent
Connected Graph
Connectedness
Connective
Connectivity of a Graph G
Connectivity Matrix
Consistency
Console
Constant
Construct
Consumable Resource
Contact Bounce
Context-Free Language (algebraic language)
Context-Sensitive Grammar
Context-Sensitive Language
Continuation
Continuous Signal System
Control Bus
Control Character
Control Circuitry
Control Cycle
Control Data Corporation
Control Design
Controlled Sharing
Controller
Control Line
Control Memory
Control Slack
Control Structure
Control Unit (CU)
Control Word
Convergence
Conversational Mode
Conversion
Convolution
Coprocessor
Copy
CORAL
Core Store
Coroutine
Corrective Maintenance
Correctness Proof
Correlation
COSMOS
Cost Function
Countable Set
Counter
Counting Problem
Coupled
Covariance
Covering

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