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Generalities.
Definition
2
.
1
.
1
Let
and
be two sets. An
application
(or a
mapping
)
from
to
is defined by a subset
such that
. We denote
.
Notation:
Given an application
:
the
domain
of
and
the
range
of
.
Remark
2
.
1
.
2
Two applications
and
are equal if, and only if, they have the same domain
, the same range
and
.
Definition
2
.
1
.
3
Let
be three sets and
and
be two applications. The
composition
of
with
is the application
such that
.
Example
2
.
1
.
4
Let
and
are given by
and
, then:
Example
2
.
1
.
5
The function
given by
is equal to
, where:
;
.
Remark
2
.
1
.
6
Generally
, even when both compositions are well-defined.
With the settings of Example
1.4
:
Thus
, according to remark
1.2
.
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Injections.
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Functions.
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Functions.
Contents
Noah Dana-Picard 2007-12-28