Definition of "countable"

Capable of being counted; having a quantity.  examples

(mathematics, of a set) finite or countably infinite; having a one-to-one correspondence (bijection) with a subset of the natural numbers.  examples

(mathematics, of a set) Countably infinite; having a bijection with the natural numbers.  examples

(grammar, of a noun) Freely usable with the indefinite article and with numbers, and therefore having a plural form.  quotations  examples

(grammar) A countable noun.  examples