proceeds as follows:

This mapping covers all such ordered pairs.

This form of triangular mapping recursively generalizes to -tuples of natural numbers, i.e., where and are natural numbers, by repeatedly mapping the first two elements of an -tuple to a natural number. For example, can be written as . Then maps to 5 so maps to , then maps to 39. Since a different 2-tuple, that is a pair such as , maps to a different natural number, a difference between two

1.Previous
3.Next