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Erschienen in:
2005 | OriginalPaper | Buchkapitel
Continuous functions
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A procedure
f
that, given
x
as input, calculates
y
as output, is called an assignment that is
defined at x
and that appoints the
value y
to the
argument x
with the notation
$$f\left( x \right) = y.$$
We say that the assignment
f
is
defined on
a set
U
, if
1.
f
is defined at
all
elements of
U
, and
2.
only
elements of
U
are allowed to be arguments of
f
.
We write
f : U → V
if and only if
f
is defined on
U
and all values of
f
are elements of
V
.