uncountability

Uncountability refers to sets of items that cannot be listed or counted one by one, even if you try forever. For example, the real numbers between 0 and 1 include many points that can't be matched one-to-one with natural numbers like 1, 2, 3, etc. This means there's no way to assign each of these numbers a unique natural number without missing some. Uncountable sets are larger and more complex than countable ones, which can be fully listed or counted, like whole numbers or basic fractions.