tétel

Tétel is a Hungarian term used primarily in mathematics to denote a proven statement or theorem. In this sense a tétel is a proposition that has been established by a formal proof, deriving its truth from axioms and previously proven results. The term is distinguished from conjectures or hypotheses, which are statements that have not yet been proven. Beyond mathematics, tétel can also mean a general assertion or proposition in logic, and in everyday language it can refer to an item, point in a list, or a claim.

In mathematical usage, a tétel is usually presented with a set of hypotheses and a conclusion, followed by a proof that shows why the conclusion necessarily follows from the hypotheses. The proof may rely on axioms, definitions, and earlier tétels, lemmas, or corollaries. Through this structure, tétels build the logical framework of a theory and are part of a cumulative chain of reasoning.

Examples commonly cited in Hungarian texts include classical theorems such as the Pythagorean theorem in geometry and Euclid’s theorem on the infinitude of primes in number theory. Such statements are treated as tétels because they are proven statements within their respective domains.

In addition to mathematics, tétel can also refer to movements or pieces in music, and to items in lists, contracts, or budgets in non-mathematical contexts. The word thus covers both specialized mathematical meaning and broader uses related to assertions, components, or sections in various fields.