countability

Countability refers to whether a set of items can be matched one-to-one with the natural numbers (1, 2, 3, ...), meaning you can list each item without missing any. A set is countable if its elements can be counted in this way—like counting numbers or books on a shelf. Uncountable sets, however, are so large that they cannot be listed completely, like the points on a line or real numbers between 0 and 1. In essence, countability measures whether a set's size can be meaningfully counted using ordinary counting methods.