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.
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