Sets of numbers have been formed in logical order. [color=#0000ff]Natural numbers[/color] ([math]\mathbb N[/math] ) express quantity. When our ancestors noticed, that decrease of quantity can be expressed with negative numbers, they had the set of [color=#0000ff]integers ([math]\mathbb Z[/math] )[/color]. Integers can be used, for example, to express rounding numbers or time before and after present. [br][br]Integers were followed by [color=#0000ff]rational numbers (or fractions)[/color] ([math]\mathbb Q[/math] ). In the past, time may have been given as [i]half of moon[/i]. Babylonians divided the circle and year to 360 parts, as it had many factors: 1, 2, 3, 4, 5, 6, 9, 10, 12,...This enabled them to solve many things exactly. Rational numbers can be either finite or infinite.[br][br]The circle gave new dimensions to the numbers. It was found, for example, that circumference of a circle cannot be solved exactly only with a radius and an angle. The missing part [math]\Large \pi[/math] is not a rational numbers but infinite and non-recurring decimal number, that is irrational number. Rational numbers and irrational numbers are called as [color=#0000ff]real numbers[/color] ([math]\mathbb R[/math] ). [br]    [br]Mathematically set of numbers are symbolized as[br][br][math]\Large\textcolor{blue}{\mathbb N = \{0,\,1,\,2,\ldots \}}\\[br]\Large\textcolor{blue}{\mathbb Z = \{\ldots,\,-1,\,-1,\,0,\,1,\,2,\,\ldots\}}\\[br]\Large\textcolor{blue}{\mathbb Q=\{\frac{m}{n}|m,n\in \cal Z,\; n\neq0\} }\\[br]\Large\textcolor{blue}{\mathbb R \Large\text{ all other real numbers besides previous, like } \pi,\,\sqrt 2,\,\sqrt[3] 5,\;\ldots} [/math][br][br]In addition to these, there is a set of complex numbers [math]\mathbb C. [/math] They are needed, for example, in electrical engineering. However, they are not the subject of this course, so they will not be covered any further.