With ordered pairs in hand, Class Comprehension enables defining functions on sets as sets of ordered pairs, making possible the next axiom:
42.
With ordered pairs in hand, Class Comprehension enables defining functions on sets as sets of ordered pairs, making possible the next axiom:
43.
A function of two or more variables is considered to have a domain consisting of ordered pairs or tuples of argument values.
44.
Since copying a pointer also copies its cell value, changing the key of the ordered pair safely disables all copies of the pointer.
45.
A " strongly connected graph " is a directed graph in which every ordered pair of vertices in the graph is strongly connected.
46.
The semantics of description logics are defined by interpreting concepts as sets of individuals and roles as sets of ordered pairs of individuals.
47.
Even those mathematical textbooks that give an informal definition of ordered pairs will often mention the formal definition of Kuratowski in an exercise.
48.
It is also sufficient to have two predicate symbols of arity 2 that define projection functions from an ordered pair to its components.
49.
Hence a type level ordered pair is two types higher than the type of its arguments and the usual Kuratowski ordered pair four types higher.
50.
Hence a type level ordered pair is two types higher than the type of its arguments and the usual Kuratowski ordered pair four types higher.
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