Arithmetic

https://en.wikipedia.org/wiki/Arithmetic

Arithmetic studies numbers and operations on numbers.

The word arithmetic comes from the Greek αριθμητική, which is a compound of ἀριθμός (number) and τέχνη, -τική (art, skill, craft).

Arithmetic studies the 4 traditional basic arithmetic operations:

• addition

• subtraction

• multiplication

• division

Since subtraction can be defined in terms of addition with inverses (i.e. negation of numbers, negative numbers), and since division can be defined in terms of multiplication with inverses (i.e. reciprocals of numbers, fractions), we can consider only these two as the most fundamental operations. Also, division can be defined in terms of repeated subtraction.

Therefore, since multiplication can be defined in terms of repeated addition, there may be only one really fundamental operations - successor, since addition can be defined in terms of repeated successor operation.

The most fundamental arithmetic operation is the successor.

Arithmetic also studies operations derived from the basic ones:

• successor

• predecessor

• addition

• subtraction

• multiplication

• factoring

• division

• divisibility

• Euclidean division

• fractions

• ratios

• reciprocal

• percentages

• exponentiation

• root

• logarithm

• percentage

• modular arithmetic

• modulo operation

• hyperoperations

• trigonometric functions

Unlike algebra that prefers variables, arithmetic deals with concrete numbers because it is more concerned with immediate results and exploring the ways in which to make more efficient calculations.

A mathematical object that supports all 4 basic arithmetic operations, with respect to a set of axioms, is called a field.