<s>
In	O
relational	B-Algorithm
algebra	I-Algorithm
,	O
a	O
projection	B-Algorithm
is	O
a	O
unary	O
operation	O
written	O
as	O
,	O
where	O
is	O
a	O
relation	O
and	O
are	O
attribute	O
names	O
.	O
</s>
<s>
Its	O
result	O
is	O
defined	O
as	O
the	O
set	O
obtained	O
when	O
the	O
components	O
of	O
the	O
tuples	B-Application
in	O
are	O
restricted	O
to	O
the	O
set	O
–	O
it	O
discards	O
(	O
or	O
excludes	O
)	O
the	O
other	O
attributes	O
.	O
</s>
<s>
In	O
practical	O
terms	O
,	O
if	O
a	O
relation	O
is	O
thought	O
of	O
as	O
a	O
table	O
,	O
then	O
projection	B-Algorithm
can	O
be	O
thought	O
of	O
as	O
picking	O
a	O
subset	O
of	O
its	O
columns	O
.	O
</s>
<s>
For	O
example	O
,	O
if	O
the	O
attributes	O
are	O
(	O
name	O
,	O
age	O
)	O
,	O
then	O
projection	B-Algorithm
of	O
the	O
relation	O
{( 	O
Alice	O
,	O
5	O
)	O
,	O
(	O
Bob	O
,	O
8	O
)	O
}	O
onto	O
attribute	O
list	O
(	O
age	O
)	O
yields	O
 { 5 , 8 } 	O
–	O
we	O
have	O
discarded	O
the	O
names	O
,	O
and	O
only	O
know	O
what	O
ages	O
are	O
present	O
.	O
</s>
<s>
Projections	B-Algorithm
may	O
also	O
modify	O
attribute	O
values	O
.	O
</s>
<s>
The	O
closely	O
related	O
concept	O
in	O
set	O
theory	O
(	O
see	O
:	O
projection	B-Algorithm
(	O
set	O
theory	O
)	O
)	O
differs	O
from	O
that	O
of	O
relational	B-Algorithm
algebra	I-Algorithm
in	O
that	O
,	O
in	O
set	O
theory	O
,	O
one	O
projects	O
onto	O
ordered	O
components	O
,	O
not	O
onto	O
attributes	O
.	O
</s>
<s>
Projection	B-Algorithm
is	O
relational	B-Algorithm
algebra	I-Algorithm
's	O
counterpart	O
of	O
existential	B-Algorithm
quantification	I-Algorithm
in	O
predicate	O
logic	O
.	O
</s>
<s>
The	O
attributes	O
not	O
included	O
correspond	O
to	O
existentially	B-Algorithm
quantified	I-Algorithm
variables	O
in	O
the	O
predicate	O
whose	O
extension	O
the	O
operand	O
relation	O
represents	O
.	O
</s>
<s>
Because	O
of	O
the	O
correspondence	O
with	O
existential	B-Algorithm
quantification	I-Algorithm
,	O
some	O
authorities	O
prefer	O
to	O
define	O
projection	B-Algorithm
in	O
terms	O
of	O
the	O
excluded	O
attributes	O
.	O
</s>
<s>
In	O
a	O
computer	O
language	O
it	O
is	O
of	O
course	O
possible	O
to	O
provide	O
notations	O
for	O
both	O
,	O
and	O
that	O
was	O
done	O
in	O
ISBL	B-Language
and	O
several	O
languages	O
that	O
have	O
taken	O
their	O
cue	O
from	O
ISBL	B-Language
.	O
</s>
<s>
A	O
nearly	O
identical	O
concept	O
occurs	O
in	O
the	O
category	O
of	O
monoids	O
,	O
called	O
a	O
string	O
projection	B-Algorithm
,	O
which	O
consists	O
of	O
removing	O
all	O
of	O
the	O
letters	O
in	O
the	O
string	O
that	O
do	O
not	O
belong	O
to	O
a	O
given	O
alphabet	O
.	O
</s>
<s>
When	O
implemented	O
in	O
SQL	B-Language
standard	O
the	O
"	O
default	O
projection	B-Algorithm
"	O
returns	O
a	O
multiset	B-Language
instead	O
of	O
a	O
set	O
,	O
and	O
the	O
projection	B-Algorithm
is	O
obtained	O
by	O
the	O
addition	O
of	O
the	O
DISTINCT	O
keyword	O
to	O
eliminate	O
duplicate	O
data	O
.	O
</s>
<s>
For	O
an	O
example	O
,	O
consider	O
the	O
relations	O
depicted	O
in	O
the	O
following	O
two	O
tables	O
which	O
are	O
the	O
relation	O
and	O
its	O
projection	B-Algorithm
on	O
(	O
some	O
say	O
"	O
over	O
"	O
)	O
the	O
attributes	O
and	O
:	O
</s>
<s>
Then	O
the	O
given	O
projection	B-Algorithm
represents	O
the	O
predicate	O
,	O
"	O
There	B-Algorithm
exists	I-Algorithm
Name	O
such	O
that	O
Name	O
is	O
age	O
years	O
old	O
and	O
weighs	O
weight.	O
"	O
</s>
<s>
More	O
formally	O
the	O
semantics	O
of	O
projection	B-Algorithm
are	O
defined	O
as	O
follows	O
:	O
</s>
<s>
The	O
result	O
of	O
a	O
projection	B-Algorithm
is	O
defined	O
only	O
if	O
is	O
a	O
subset	O
of	O
the	O
header	O
of	O
.	O
</s>
<s>
Projection	B-Algorithm
over	O
no	O
attributes	O
at	O
all	O
is	O
possible	O
,	O
yielding	O
a	O
relation	B-Algorithm
of	I-Algorithm
degree	I-Algorithm
zero	I-Algorithm
.	O
</s>
