The Universal Computer

Cantor: Detour through Infinity

set.

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For example, if one observes that there are no empty seats and no

standees in an auditorium, then one can conclude (without counting) that

the number of people in the audience and the number of seats are the

same—one is matching up each seat with the person occupying it. Leibniz

held that if such things as infinite numbers did exist, then the same idea

should apply to them: if a one-one matching can be defined between two

infinite sets, then one should be able to conclude that the two sets have the

same number of members. Then, he proposed to apply this concept to the

following two sets: the set of all natural numb