Number systems
Number systems
- About the numerical sets used in our numbering system
In our numbering system, there are several numerical sets (Ditutor, n.d.) or number systems, all of them infinite, this means that there are larger infinities that contain smaller infinities, as happens, for example, with the system of natural numbers (EcuRed, n.d.), which is absorbed by that of the cardinals. and this in turn is absorbed by that of the integers.
1) Natural Numbers (N)
They are whole numbers from infinity, serve to account for things and is the most intuitive set.
N = {1, 2, 3, 4, 5, 6, 7, .......}
2) Cardinal Numbers (N *)
It is the union of natural numbers with 0.
N * = {0, 1, 2, 3, 4, 5, 6, .....}
3) Fractional (Q +)
It was born because of the need to divide the cardinal numbers, so these are a subset of the fractionals.
Q + = {0, ½, 2, 3/4 3, 9/7, .....}
4) Integers (Z)
This system was born to give a solution to the subtraction or subtraction, this includes the negative integers and positive or natural integers and zero, in other words, the set of cardinals is a subset of the integers.
Z = {..... –3, -2, -1, 0, 1, 2, 3, ...}
5) Rational Numbers (Q)
Rational numbers, born in response to the limitations presented by the previous sets, are constructed from integers and include negative, positive and zero fractional numbers.
Q = {....- ¾, - ½, - ¼, 0, ¼, ½, ¾, .....}
6) Irrational Numbers (I)
This set includes all numbers that have infinite decimals, such as √2, the number pi or the number e.
7) Set of Real Numbers (R)
Real numbers are the result of the union between the set of rational and irrational.
R = {....- 10, -1, - ¾, - ½, - ¼, 0, ¼, √2, 5, .....}
8) Set of Imaginary Numbers (i)
They are born in response to the roots of negative numbers. They are denoted by i and their unit is
√-1, so: i = √-1.
9) Set of Complex Numbers (C)
It is the union of real numbers with imaginary numbers.
They are whole numbers from infinity, serve to account for things and is the most intuitive set.
N = {1, 2, 3, 4, 5, 6, 7, .......}
2) Cardinal Numbers (N *)
It is the union of natural numbers with 0.
N * = {0, 1, 2, 3, 4, 5, 6, .....}
3) Fractional (Q +)
It was born because of the need to divide the cardinal numbers, so these are a subset of the fractionals.
Q + = {0, ½, 2, 3/4 3, 9/7, .....}
4) Integers (Z)
This system was born to give a solution to the subtraction or subtraction, this includes the negative integers and positive or natural integers and zero, in other words, the set of cardinals is a subset of the integers.
Z = {..... –3, -2, -1, 0, 1, 2, 3, ...}
5) Rational Numbers (Q)
Rational numbers, born in response to the limitations presented by the previous sets, are constructed from integers and include negative, positive and zero fractional numbers.
Q = {....- ¾, - ½, - ¼, 0, ¼, ½, ¾, .....}
6) Irrational Numbers (I)
This set includes all numbers that have infinite decimals, such as √2, the number pi or the number e.
7) Set of Real Numbers (R)
Real numbers are the result of the union between the set of rational and irrational.
R = {....- 10, -1, - ¾, - ½, - ¼, 0, ¼, √2, 5, .....}
8) Set of Imaginary Numbers (i)
They are born in response to the roots of negative numbers. They are denoted by i and their unit is
√-1, so: i = √-1.
9) Set of Complex Numbers (C)
It is the union of real numbers with imaginary numbers.
References:
Ditutor. (s.f.). Conjuntos numéricos. Recuperado de https://www.ditutor.com/numeros_naturales/conjuntos_numericos.html
EcuRed. (s.f.). Conjuntos numéricos. Recuperado de https://www.ecured.cu/Conjuntos_numéricos
EcuRed. (s.f.). Conjuntos numéricos. Recuperado de https://www.ecured.cu/Conjuntos_numéricos
How to cite this article:
Nocetti, F.A. (2019). "Number systems". In NabbuBlog. Retrieved from http://nabbublog.blogspot.com/2019/01/number-systems.html