| 21. | Hence the ordered pair can be taken as a primitive notion, whose associated axiom is the characteristic property.
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| 22. | The Digram Round contains a tile representing an ordered pair of letters, which is regarded as a single unit.
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| 23. | Back-substituting the second ordered pair gives us x + y = 55, xy = 16, which gives no solutions.
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| 24. | Another way to rigorously deal with ordered pairs is to define them formally in the context of set theory.
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| 25. | The locks-and-keys approach represents pointers as ordered pairs ( key, address ) where the key is an integer value.
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| 26. | Then one way of representing the truth condition of " Nixon is alive " is as the ordered pair.
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| 27. | Where " A " is a 2? orthogonal matrix and is an arbitrary ordered pair of numbers; that is,
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| 28. | For example, the ordered pair ( 0, 1 ), in the usual construction of the complex numbers with two-dimensional vectors.
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| 29. | For an extensive discussion of the ordered pair in the context of Quinian set theories, see Holmes ( 1998 ).
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| 30. | For additional clarification, the ordered pair may be denoted by the variant notation, but this notation also has other uses.
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