Document frequency (${\mathrm{df}}_t$)

The document frequency ${\mathrm{df}}_t$ of term $t$ is the number of documents in a specified collection that contain it at least once. Repeating a term many times inside one document contributes only one to its document frequency.^[ref]

For a collection $D$, write the count using an indicator function:Here ${\mathrm{tf}}_{t,d}$ is the raw term frequency. When an inverted index has one document record per containing document, the number of those records in the term's postings list equals ${\mathrm{df}}_t$. A record's position list can still contain several occurrences.

Consider red red boat, boat red red and blue boat. Red occurs four times but has document frequency two. Boat occurs only three times but has document frequency three. Thus the term with more total occurrences need not appear in more documents. Blue has document frequency one.

Adding another hundred red occurrences to the first document increases its term frequency without changing red's document frequency. Adding a new document containing red increases the latter by one. The collection boundary and preprocessing rules are therefore part of the statistic's definition. In information retrieval, this distinction lets scoring use evidence about how widely a term is distributed, rather than confusing repetition in one document with coverage of many documents.