Definition:Increasing
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[edit] Ordered Sets
Let
and
be posets.
Let
be a mapping.
Then
is increasing iff:
Alternative terms are order-preserving, isotone and non-decreasing.
Note that this definition also holds if
.
[edit] Note
Some sources insist at the point of definition that
be an injection for it to be definable as order-preserving, but this is conceptually unnecessary.
[edit] Real Functions
This definition continues to hold when
.
Thus, let
be a real function.
Then
is increasing iff:
[edit] Sequences
Let
be a sequence in
.
Then
is increasing iff:
.
[edit] Also see

