arithmetic

Before entering fully into the clarification of the meaning of the term arithmetic, we are going to analyze what is its etymological origin. Specifically, we can say that it is a word that comes from the Latin noun “arithmetica”. However, this, in turn, derives from the Greek, exactly from “aritmetikos”, which is the result of the sum of two differentiated parts:
-The name “arithmos”, which can be translated as “number”.
-The suffix “-tikos”, which is used to indicate “relative to”.

The arithmetic is the area of ​​the math focused on numbers And in the operations that are done with them. It should be remembered that numbers are the signs that allow us to express a quantity.

The formal emergence of arithmetic took place in the Ancient Greece from an increase in the rigor of mathematics and the development of proofs. Thus the four elementary operations of this branch were established: Add, subtract, multiply Y divide.

Advancing in the complexity of arithmetic, one can go from elementary operations to others such as the extraction of estate and the calculation of powers. It is also possible to include letters together with the numbers in order to achieve the representation of different variables.

Among the most important figures in arithmetic in Ancient Greece, we can highlight some such as the following:
-Euclides (325 BC - 265 BC), who is considered the father of Geometry. He made numerous works that have become pillars of the aforementioned arithmetic, as would be the case of "The elements".
-Nicomachus of Gerasa, who is listed as a Neo-Pythagorean mathematician. One of his most important and recognized works was "Introduction to arithmetic", where, among other things, he comes to leave the theory of numbers on the table and well explained. So important was this work that it became manual in the Platonic schools.

The arithmetic calculations they can develop in different ways. In the case of simple operations, they can be carried out mentally or with the help of the fingers of the hand. In ancient times the abacus, a device with small balls that move to do the calculations. Currently arithmetic operations are usually carried out with a calculator, either physical or virtual.

Although it is true that the abacus is one of the best known instruments that have been used to carry out calculations within arithmetic, in history there have been and there are many others with the same objective. We are referring to the counting sticks, the Babylonian tablet, the Inca abacus, the adding machine ...

It is known as high arithmetic to the study of the properties and functions of numbers. In this framework, one can speak of the binary arithmetic (which appeals to zero and one to represent values), the modular arithmetic (that works with modules) and the ordinal arithmetic (oriented to ordinal numbers), among others.

The second order arithmetic, on the other hand, it is composed of different axiomatic systems that allow the formalization of the natural numbers and of the subsets formed by these.