2.1. Countable Infinity

Example: Countable Chairs

Suppose you are standing in an empty classroom, with a lot of students waiting to get in. How can you know whether there are enough chairs for everyone? Use the mathematical definition of cardinality to determine the answer.
We can not count the students, since they are moving around too much. Therefore, we set up a function f that associates each chair with a student by simply asking each student to find a chair and sit down. If all chairs are taken, and no students are left standing, then what does this mean for our function f ? Therefore, the function f is a bijection between the domain and the range, and by definition of cardinality the number of students matches the number of chairs, i.e. both sets have the same cardinality.

On the other hand, if the two sets did not contain the same number of elements, the following could happen:

Next | Previous | Glossary | Map