tælling

Tælling is the act of determining how many elements exist in a set or how often an event occurs. In Danish, the verb tælle means to count, and tælling is the corresponding noun. Counting is a basic cognitive and practical activity that spans everyday tasks, scientific work, and formal methods, from tally marks to automated counters in software.

In mathematics, tælling refers to enumeration and combinatorics — counting objects under constraints and calculating how many distinct arrangements or selections are possible. Classic tools include the product rule and the sum rule, which allow counting complex configurations by combining simpler choices. For example, the number of ways to choose k items from n is given by binomial coefficients C(n, k).

Statistics and data collection treat counts as a type of data called count data. Counts measure how many times a category occurs and underpin frequency distributions, proportions, and basic estimations. When populations are large, counts are often obtained through sampling or measurement rather than full enumeration.

In computing and data processing, counting is a fundamental operation performed by loops, counters, and aggregators. Count information supports algorithms, resource monitoring, and reporting. In everyday use, counting enables budgeting, inventory, census-taking, and other decision-making tasks.

Counting is a universal concept with roots in ancient practices and remains essential across disciplines, including mathematics, statistics, and computer science.