mittenegatiivsed

Mittenegatiivsed is a term used in Estonian mathematics to describe quantities that are not negative; that is, values greater than or equal to zero. When applied to real numbers, the mittenegatiivsete reaalarvude kogumi is the interval [0, ∞), sometimes denoted R≥0 or R+, although notation varies. The concept also applies to vectors, matrices, functions, or sequences whose every entry or value is nonnegative.

Properties and basic facts: The set of mittenegatiivsed numbers is closed under addition and multiplication: if a ≥ 0 and b ≥ 0, then a + b ≥ 0 and ab ≥ 0. Zero is mittenegatiivne, and positive numbers satisfy the same nonnegativity condition. The term is contrasted with 'negatiivne' (negative) and 'positiivne' (positive), the latter typically meaning strictly greater than zero.

Examples: 0, 2, 3.5 are mittenegatiivsed real numbers; −1 is not. A vector such as (1, 0, 4) is mittenegatiivne because all components are nonnegative.

Applications: In probability and statistics, probabilities are mittenegatiivsed; in geometry and measurement, lengths, areas, and other measures are nonnegative by definition. In optimization, nonnegativity constraints are common, for example x ≥ 0 componentwise in linear programming. In higher dimensions, the mittenegatiivsete elements form the nonnegative orthant.

Relations and variants: For any real x, x² is mittenegatiivne, and |x| ≥ 0 with equality only at x = 0. The term also appears in phrases such as mittenegatiivsed arvud (nonnegative numbers), mittenegatiivsed täisarvud (nonnegative integers), and mittenegatiivsed reaalarvud (nonnegative real numbers).