Editing Finitary relation (section)

== Example ==
Consider the ternary relation ''R'' "''x'' thinks that ''y'' likes ''z''" over the set of people {{nowrap|1=''P'' = {{mset| Alice, Bob, Charles, Denise }}}}, defined by:
: {{nowrap|1=''R'' = {{mset| (Alice, Bob, Denise), (Charles, Alice, Bob), (Charles, Charles, Alice), (Denise, Denise, Denise) }}}}.

''R'' can be represented equivalently by the following table:

{| class="wikitable" style="width: 25em; margin: 0.5em auto; text-align: center;"
|+ Relation ''R'' "''x'' thinks that ''y'' likes ''z''"
|-
! ''x'' !! ''y'' !! ''z''
|-
| Alice || Bob || Denise
|-
| Charles || Alice || Bob
|-
| Charles || Charles || Alice
|-
| Denise || Denise || Denise
|}

Here, each row represents a triple of ''R'', that is it makes a statement of the form "''x'' thinks that ''y'' likes ''z''". For instance, the first row states that "Alice thinks that Bob likes Denise". All rows are distinct. The ordering of rows is insignificant but the ordering of columns is significant.{{sfn|ps=|Codd|1970}}

The above table is also a simple example of a [[relational database]], a field with theory rooted in [[relational algebra]] and applications in data management.<ref>{{cite web|url=http://www.pitt.edu/~bonidie/cs441/relations.pdf|title=Relations – CS441|website=www.pitt.edu|access-date=2019-12-11}}</ref> Computer scientists, logicians, and mathematicians, however, tend to have different conceptions what a general relation is, and what it is consisted of. For example, databases are designed to deal with empirical data, which is by definition finite, whereas in mathematics, relations with infinite arity (i.e., infinitary relation) are also considered.