<s>
In	O
mathematics	O
,	O
the	O
range	B-Algorithm
of	I-Algorithm
a	I-Algorithm
function	I-Algorithm
may	O
refer	O
to	O
either	O
of	O
two	O
closely	O
related	O
concepts	O
:	O
</s>
<s>
The	O
sets	O
and	O
are	O
called	O
domain	B-Algorithm
and	O
codomain	B-Algorithm
of	O
,	O
respectively	O
.	O
</s>
<s>
Older	O
books	O
,	O
when	O
they	O
use	O
the	O
word	O
"	O
range	O
"	O
,	O
tend	O
to	O
use	O
it	O
to	O
mean	O
what	O
is	O
now	O
called	O
the	O
codomain	B-Algorithm
.	O
</s>
<s>
with	O
domain	B-Algorithm
,	O
the	O
range	O
of	O
,	O
sometimes	O
denoted	O
or	O
,	O
may	O
refer	O
to	O
the	O
codomain	B-Algorithm
or	O
target	B-Algorithm
set	I-Algorithm
(	O
i.e.	O
,	O
the	O
set	O
into	O
which	O
all	O
of	O
the	O
output	O
of	O
is	O
constrained	O
to	O
fall	O
)	O
,	O
or	O
to	O
,	O
the	O
image	O
of	O
the	O
domain	B-Algorithm
of	O
under	O
(	O
i.e.	O
,	O
the	O
subset	O
of	O
consisting	O
of	O
all	O
actual	O
outputs	O
of	O
)	O
.	O
</s>
<s>
The	O
image	O
of	O
a	O
function	O
is	O
always	O
a	O
subset	O
of	O
the	O
codomain	B-Algorithm
of	O
the	O
function	O
.	O
</s>
<s>
In	O
this	O
case	O
,	O
its	O
codomain	B-Algorithm
is	O
the	O
set	O
of	O
real	O
numbers	O
,	O
but	O
its	O
image	O
is	O
the	O
set	O
of	O
non-negative	O
real	O
numbers	O
,	O
since	O
is	O
never	O
negative	O
if	O
is	O
real	O
.	O
</s>
<s>
For	O
this	O
function	O
,	O
if	O
we	O
use	O
"	O
range	O
"	O
to	O
mean	O
codomain	B-Algorithm
,	O
it	O
refers	O
to	O
;	O
if	O
we	O
use	O
"	O
range	O
"	O
to	O
mean	O
image	O
,	O
it	O
refers	O
to	O
.	O
</s>
<s>
In	O
many	O
cases	O
,	O
the	O
image	O
and	O
the	O
codomain	B-Algorithm
can	O
coincide	O
.	O
</s>
<s>
For	O
this	O
function	O
,	O
the	O
codomain	B-Algorithm
and	O
the	O
image	O
are	O
the	O
same	O
(	O
both	O
being	O
the	O
set	O
of	O
real	O
numbers	O
)	O
,	O
so	O
the	O
word	O
range	O
is	O
unambiguous	O
.	O
</s>
