Addisyon

Addisyon, or addition, is a basic mathematical operation that combines two or more numbers to produce their sum. It is denoted by the plus sign (+) and is defined within a given number system. The result is called the sum. Addition applies to integers, rational numbers, real numbers, complex numbers, and can be extended to vectors, matrices, and other mathematical objects.

For two numbers a and b, the result is a + b. For more addends, a1 + a2 + ... + an equals their total. The operation has several fundamental properties: closure within the chosen set, the commutative property (a + b = b + a), the associative property ((a + b) + c = a + (b + c)), and an identity element 0 (a + 0 = a). Subtraction serves as the inverse operation, with a − b equal to a + (−b).

In base-10 arithmetic, addition proceeds by aligning digits by place value, adding from right to left, and carrying when a sum exceeds 9. The same method generalizes to other bases, using base b and carries when sums reach b.

In computing, addition is implemented with circuits such as half adders and full adders, and various adder architectures (e.g., ripple-carry and carry-lookahead adders) enable fast binary addition.

Historically, addition is among the oldest arithmetic operations, evidenced in ancient Mesopotamian and Egyptian mathematics. The development of Hindu-Arabic numerals and the concept of zero facilitated more systematic and scalable addition.

Addisyon remains essential in everyday counting, accounting, algebra, and scientific computation, serving as the foundation for more complex operations such as multiplication, calculus, and data analysis.