31. But if you asked what ordered pairs the set contains, you'd get three things that claimed they were in it. 32. For some input ordered pairs , one of the below can be calculated . ( The availability differs from modes .) 33. In the other definition a function is defined as a set of ordered pairs where each first element only occurs once. 34. However, this approach also has its drawbacks as both the existence of ordered pairs and their characteristic property must be axiomatically assumed. 35. Otherwise, it is called a " weakly connected graph " if every ordered pair of vertices in the graph is weakly connected. 36. Formally, a metric space is an ordered pair ( M, d ) where M is a set and d is a function 37. As shown below, Norbert Wiener ( 1914 ) reduced the notion of relation to class by his definition of an ordered pair . 38. In addition to his work in geometry, Bolyai developed a rigorous geometric concept of complex numbers as ordered pairs of real numbers. 39. This is a function of arity 2 that takes pairs of elements of the domain and returns an ordered pair containing them. 40. In that dissertation, he was the first to state publicly that ordered pairs can be defined in terms of elementary set theory.
