Cocountability

In mathematics, a cocountable subset of a set ${\displaystyle X}$ is a subset ${\displaystyle Y}$ whose complement in ${\displaystyle X}$ is a countable set. In other words, ${\displaystyle Y}$ contains all but countably many elements of ${\displaystyle X}$. Since the rational numbers are a countable subset of the reals, for example, the irrational numbers are a cocountable subset of the reals. If the complement is finite, then one says ${\displaystyle Y}$ is cofinite.