> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/350-type-theory/basic-concepts/about-types.md). # Types * The *concept of types* was conceived as a way to avoid set-theoretical paradoxes. * A *type system* is a formal system in which every term has a property called "type", which defines a term's meaning (and operations that may be performed on it). * A *data type* is a collection of values used for computations. * *Typification*, a process of creating standard (typical) social construction based on standard assumptions * In model theory, a *type is an object* that describes how a collection of elements in a mathematical structure might *behave*. * A *data structure* is a data organization, management and storage format that enables efficient access and modification of data. * A data structure is a collection of data, plus relations between the data, plus the applicable operations. * A data structure is an algebraic structure about data. * *Typology* is the study of types or the systematic classification of the types of something according to their common characteristics. Typology is the act of finding, counting and classification facts with the help of eyes, other senses and logic. Typology may refer to: * Typology in linguistics classifies languages wrt to their structural features * Typology in psychology models personality types * Psychological typologies are classes of distinctions between people * Sociopolitical typology counts 4 types of a political organization * *Categorization*, one of the most fundamental cognitive abilities, is the activity of recognizing shared features or similarities between the elements of the experience of the world (such as objects, events, or ideas), organizing and classifying experience by associating them to a more abstract group (that is, a category, class, or type),on the basis of their traits, features, similarities or other criteria. Categorization is considered , * Etymology: from Middle English type ("symbol, figure, emblem"), from Latin typus, from Ancient Greek τύπος (túpos, "mark, impression, type"), from τύπτω (túptō, "I strike, beat"). ## Ref