Natural number


The natural numbers are the figures that are used for the most basic calculation operations, as well as to count the elements belonging to any set. Similarly, it can be defined as any constituent of the set ℕ or ℕ = {1, 2, 3, 4,…}; It should be noted that, depending on the scientific area with which you work, this definition may or may not include zero, that is, ℕ = {0, 1, 2, 3, 4,…}. According to its organization, the number on the right is the successive or next one, while the one on the left will be the regressive one, although this is more common when they are counted in the same way.

In the ancient Greco-Roman world, the representation of numerical quantities was relegated to the use of the symbols of the alphabet; later, new symbols would be included. However, it was not until the 19th century that the mission to discover if natural numbers really existed began; Richard Dedekind was the man who was in charge of elaborating a series of theories to verify the existence of the set. This caused various intellectuals and mathematicians of the time, such as Giuseppe Peano, Friedrich Ludwig Gottlob Frege and Ernst Zermelo, who ended up establishing the group within science and assigning it a series of characteristics.

These types of numbers are normally used to count the components of a set of elements; this, knowing that this set is a collection of objects, such as routes, figures, letters, numbers or people, which can be considered as an object itself. These are identified with certain letters, usually according to the name they receive. The natural numbers, likewise, have a series of properties, such as: it is a completely and well-ordered set, due to its succession relationship; the quantities corresponding to q and r will always be determined by a and b. In addition to this, every number greater than 1 must go after another natural number; that between two natural numbers, there is a finite quantity and that there will always be a number greater than another or, being the same, it is infinite.