From Wiktionary, the free dictionary

From Middle English countable, equivalent to count (“to enumerate”) +‎ -able.

• IPA^(key): /ˈkaʊn.tə.bəl/
• (US) IPA^(key): /ˈkaʊn.tə.bəl/, [ˈkʰãʊ̯̃n.(ɾ)ə.bɫ̩]
• Rhymes: -aʊntəbəl
• Hyphenation: count‧a‧ble

countable (not comparable)

2. Capable of being counted; having a quantity.

   Antonyms: uncountable, countless, numberless, innumerable; see also Thesaurus:innumerable

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

   Antonyms: uncountable, infinite

   Hypernyms: finite, countably infinite

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

      Synonym: denumerable

      Antonyms: uncountable, non-denumerable

6. (grammar, of a noun) Freely usable with the indefinite article and with numbers.

   Synonym: count

   Antonyms: uncountable, noncount, non-count

   • 2014, James Lambert, “Diachronic stability in Indian English lexis”, in World Englishes, page 112:

     In these extracts the word abuse is used in the sense of ‘an individual piece of invective’ or ‘an abusive comment’ and is clearly a countable noun.

• The mathematics sense by which finite sets are countable is more common than the sense by which finite sets are not countable. To avoid ambiguity, the terms at most countable or countably infinite may be used.

• countability

countable (plural countables)

2. (grammar) A noun that is countable.

   Synonyms: count noun, countable noun

   Antonyms: uncountable, mass noun, noncount noun, non-count noun, uncountable noun