User:Phlsph7/Arithmetic - Definition, etymology, and related fields

Definition, etymology, and related fields
Arithmetic is the fundamental branch of mathematics that studies numbers and their operations. In particular, it deals with numerical calculations using the arithmetic operations of addition, subtraction, multiplication, division, exponentiation, and logarithm. The term "arithmetic" has its root in the Latin term "" which derives from the Ancient Greek words (arithmos), meaning "number", and   (arithmetike tekhne), meaning "the art of counting".

There are disagreements about its precise definition. According to a narrow characterization, arithmetic deals only with natural numbers. However, the more common view is to include operations on integers, rational numbers, real numbers, and sometimes also complex numbers in its scope. Some definitions restrict arithmetic to the field of numerical calculations. When understood in a wider sense, it also includes the study of how the concept of numbers developed, the analysis of properties of and relations between numbers, and the examination of the axiomatic structure of arithmetic operations.

Arithmetic is closely related to number theory and some authors use the terms as synonyms. However, in a more specific sense, number theory is restricted to the study of integers and focuses on their properties and relationships such as divisibility, factorization, and primality. Traditionally, it is known as higher arithmetic. Arithmetic is intimately connected to many branches of mathematics that depend on numerical operations. Algebra relies on arithmetic principles to solve equations using variables. These principles also play a key role in calculus in its attempt to determine rates of change and areas under curves. Geometry uses arithmetic operations to measure the properties of shapes while statistics utilizes them to analyze numerical data.