Optellen

Optellen, the Dutch term for addition, is a fundamental arithmetic operation that combines numbers to produce a total. In mathematics, the operation is written as a + b, and the result is called the sum. Optellen applies to various number systems, including integers, rational, real, and complex numbers, and extends to more advanced contexts such as vectors and matrices.

Two key properties organize addition: commutativity and associativity. Commutativity means that a + b = b + a, while associativity means that (a + b) + c = a + (b + c). The additive identity is 0, since a + 0 = a for any number a. Addition is closed within its domain, meaning the sum of numbers from the domain is again a member of that domain. In decimal arithmetic, addition proceeds by aligning digits by place value and summing from the right, carrying when a column sums to ten or more.

Examples illustrate these ideas: 3 + 5 = 8; 27 + 46 = 73; -4 + 7 = 3. Adding more than two numbers is done by repeated application, as in a + b + c. Optellen is foundational for counting, budgeting, measurements, and more complex mathematics, including fractional arithmetic and vector addition. The term itself derives from Dutch, with "tellen" meaning to count and "op" indicating summing up.