Gemengdinteger

Gemengdinteger is not a standard mathematical term in Dutch. In practice, the phrase is sometimes used informally to refer to two related concepts in mathematics and optimization: mixed numbers (gemengde getallen) and mixed-integer programming. The exact meaning depends on the context.

In the context of numbers, a gemengd getal (mixed number) is a number that combines an integer part with a proper fraction. For example, 5 3/4 represents five plus three quarters, and it is equal to the improper fraction 23/4. Conversion between mixed numbers and improper fractions is straightforward: to convert a mixed number a b/c to an improper fraction, compute a×c + b over c; to convert back, divide the numerator by the denominator to obtain the integer part and remainder.

In optimization, the Dutch term for mixed-integer programming is gemengde-integer programmering or gemengd-integer programmering. A mixed-integer programming problem involves decision variables some of which must take integer values while others are allowed to be continuous. This framework is used for problems in scheduling, logistics, and resource allocation. Mixed-integer problems are typically solved using strategies such as branch-and-bound, cutting planes, and heuristic methods, often with specialized software.

Spelling and usage notes: the standard Dutch terms are gemengd getal for mixed numbers and gemengde-integer programmering (or gemengd-integer programmering) for the optimization context. When encountered as a single word, gemengdinteger is likely a shorthand or translation artifact rather than a formal term.

See also: mixed number, improper fraction, mixed-integer programming, integer programming.