Zählung

Zählung is a German term meaning the act of counting or enumerating items. It denotes both the process of determining how many elements a set contains and the result, the count or tally. In everyday language, it can refer to counting objects, votes, or events, as well as to an official census.

In mathematics, Zählung describes determining the size of a finite set by counting its elements. The size is called the cardinality. For finite sets, counting suffices to assign a natural number to the set. For infinite sets, mathematicians speak of cardinality through a one-to-one correspondence with the natural numbers, rather than a finite count; the term Zählung is sometimes used informally to describe these processes.

In statistics and demography, Zählung is common in contexts such as population counts or event tallies. A Volkszählung (census) collects demographic, social, and economic data to enumerate a population and understand its structure.

In practical usage, Zählung appears in phrases like die Zählung der Stimmen (counting of votes) or eine Zählung von Objekten. The related term Zähler denotes a counter device or a person performing the count.

Zählung is also used in music to indicate counting measures and beats, e.g., counting eins, zwei, drei, vier to organize rhythm. The exact sense of Zählung depends on context: mathematics, statistics, linguistics, or daily language.