optelsom

Optelsom is a Dutch mathematical term that refers to the sum resulting from adding two or more numbers. It can describe both the act of addition and the final value produced. In many contexts optelsom is synonymous with the terms som or optelling of numbers, and it is a fundamental concept in arithmetic and algebra.

The operation of addition is commutative, meaning that the order of the addends does not affect the result (a + b = b + a), and it is associative, so (a + b) + c = a + (b + c). The additive identity is 0, since a + 0 = a for any number a, and every number has an additive inverse, -a, with a + (-a) = 0.

Calculation and notation: The optelsom of a finite list of numbers a1, a2, ..., an is a1 + a2 + ... + an. It is commonly written with summation notation ∑_{i=1}^n a_i. Example: 7 + 12 = 19; 2 + 4 + 6 + 8 = 20. For sequences, the partial sums S_k = ∑_{i=1}^k a_i describe the running total.

Extensions and applications: Optelsom applies to real numbers, integers, fractions, and complex numbers, and extends to vector or matrix addition (performed componentwise). It underlies many procedures such as calculating totals in data sets, computing averages, and generating checksums. In analytic contexts, formulas for arithmetic series summarize sums of evenly spaced terms.

See also: summation, sigma notation, cumulative sum, arithmetic series, additive identity.