Aritmeetika

Aritmeetika, or arithmetic, is a branch of mathematics concerned with numbers and the basic rules for combining them through addition, subtraction, multiplication, and division. It forms the foundation for most everyday mathematical calculations and for more advanced areas of mathematics. Arithmetic studies the properties of these operations across various number systems, including natural numbers, integers, rational numbers, real numbers, and, in broader treatments, complex numbers.

Key concepts include the order of operations, place value, and the use of identities such as the additive identity (0) and the multiplicative identity (1). The standard properties of arithmetic—commutativity (a + b = b + a, a × b = b × a), associativity ((a + b) + c = a + (b + c), (a × b) × c = a × (b × c)), and distributivity (a × (b + c) = a × b + a × c)—govern how numbers can be rearranged during calculations. Algorithms such as long addition, subtraction, multiplication, and division provide systematic methods to compute results.

Historically, arithmetic arose from practical counting in ancient civilizations and evolved with the development of numeral systems, notably the base-10 positional system and the concept of zero. Its techniques have been refined through centuries and underpin the formal study of mathematics.

Applications are widespread, including finance, measurement, engineering, science, and computer science, where arithmetic operations are fundamental to data processing and algorithm design. Arithmetic also serves as the starting point for learning algebra and number theory, bridging concrete calculations and abstract reasoning.