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