zählbar

Zählbar is a German adjective meaning countable. It describes nouns or items that can be counted as discrete units. Examples are simple quantities such as ein Apfel and zwei Äpfel. The opposite is unzählig or unzählbar, used for substances or masses that are not typically counted individually. In practice, many mass nouns are considered unzählbar, though contexts with containers or measures can make them countable, for example durch Mengeneinheiten or Behälterbezeichnungen like ein Glas Wasser or zwei Flaschen Wein.

In grammar, zählbar refers to countable nouns (zählbare Substantive) in contrast to unzählbare (uncountable) nouns. Countable nouns allow singular and plural forms and are counted directly with numerals or indefinite articles: ein Hund, zwei Hunde. Unzählbare nouns generally do not have a plural in direct counting, but they can be quantified with measure words or expressions like viel Wasser, wenig Geld. The distinction helps determine agreement, article use, and numerals in German.

In mathematics, zählbar denotes a property of sets. A set is countable if it is finite or has the same cardinality as a subset of the natural numbers, i.e., there exists a bijection between the set and a subset of N. Equivalently, there is a surjection from N onto the set. Countable infinite sets are called abzählbar (denumerierbar). Examples of countable sets are N, Z, and Q, while R (the real numbers) is unzählbar (uncountable).

Usage of zählbar is common in technical, linguistic, and mathematical contexts; in everyday language, speakers may refer to "zählbare Gegenstände" or "zählbare Mengen" when appropriate.