Alapfeltétel

Alapfeltétel is a term used in Hungarian mathematics and related fields to denote a basic condition that must be satisfied for a statement, theorem, or construction to hold. In many contexts it corresponds to a necessary condition: if the alapfeltétel is violated, the conclusion cannot be true. It is not, however, necessarily sufficient on its own; meeting the alapfeltétel may be required but not enough to guarantee the result.

Distinction from related terms

- Necessary condition: an alapfeltétel is often a necessary condition, meaning its failure rules out the possibility of the statement being true.

- Sufficient condition: a condition under which the statement is guaranteed is called an elégséges vagy elégséges feltétel. An alapfeltétel may be necessary without being sufficient.

- Precondition: in programming and problem solving, alapfeltétel is closely related to the idea of a precondition that must hold before a procedure or argument can be correctly applied.

Common examples

- In calculus, differentiability at a point implies continuity there; thus continuity is a necessary condition for differentiability.

- In geometry, the side lengths a, b, c can form a non-degenerate triangle only if the triangle inequalities hold (a + b > c, etc.); otherwise a triangle cannot exist.

- In algorithms, a function may require certain preconditions (such as a non-empty input array) as alapfeltételei for correct execution; if these conditions are not met, the behavior may be undefined.

Usage and placement

Alapfeltétel is typically stated at the outset of a problem or theorem as a condition assumed to be true for the discussion that follows. It helps delineate the scope of a result and clarifies what must be verified before applying a method or claim. See also: szükséges feltétel, elégséges feltétel, precondition.