Bags, sets and the δ and γ operators
Bags and sets
Bag
and
Set
:
Set
= a
collection
of
elements
that
do
not
contain
duplicate
elements
Example:
S = { 1, 2, 3 }
Bag
= a
collection
of
elements
that
can
contain
duplicate
elements
Example:
B = { 1,
2, 2,
3 }
Relations
in (1) Relational Algebra and in (2) a database system
Recall:
a
relation
per
definition
Relation
in
Relational Algebra
(a
mathematical language
) is a
set
of
tuples
A
set
does
not
have
duplicate values
Database systems
:
All
database systems
implement a
relation
as a
bag
of
tuples
Because:
Detecting/Removing
duplicate values
requires
extra overhead
No extra work
is
performed
to
check/remove
duplicate values
by default
Users
can
request
the
database system
to
remove duplicates
using the
"duplicate elimiation" operation
The duplicate elimination operator δ
δ
:
remove duplicates
δ(B)
= the
set of tuples
in
(bag)
B
with
duplicates
removed
Example:
δ({1,
2, 2
, 3})
=
{1,
2
, 3}