suchthat

Suchthat is not a standalone technical term in mathematics or logic. Rather, it refers to the common English phrase “such that,” which is used to introduce a condition or predicate that elements must satisfy. In mathematical writing, this phrasing helps connect a set, relation, or function to the constraints that define it.

In set-builder notation, “such that” is often rendered implicitly by punctuation or symbols. For example, the set {x ∈ R : x^2 < 4} is typically read as “the set of all x in R such that x^2 is less than 4.” In many texts, the colon or a vertical bar serves the same function, replacing the words “such that.” The phrase itself functions as a linguistic bridge rather than as a formal operator.

In logical descriptions, authors may use “such that” to explain existential or universal quantifications in natural language, e.g., “There exists x such that x^2 = 2.” In formal logic, these ideas are expressed with quantifiers (exists, for all), but “such that” remains common in expository writing to specify the conditions involved.

Variants and related phrases include “for which,” “with the property that,” and “subject to.” While the connective is essential for clarity in explanation, many disciplines favor compact symbolic notation in formal statements, reserving “such that” for narrative or introductory passages.