Numerical sets are one of the fundamental concepts in all scientific sciences, and numbers are the basic bricks from the complex mathematical theory has been developed.
Natural numbers are the most simple and intuitive ones. They have been called natural after the fact that they are immediately perceivable by the study of the Nature that surrounds us. They are somewhat related to machine learning in the sense that they can be used to enumerate patterns that we perceive as identical (e.g. apples, dogs, etc.). The set of natural numbers is described with the letter $\mathbb{N}$.
Starting from natural numbers we can extend progressively our numerical set to include new elements. For example, while the sum of every pair of natural number is still a natural number, the subtraction is not. Starting from this consideration, we can build a new set where the subtraction of two elements is always admitted. Such set is that of integer numbers. Examples of integer numbers are $1$, $2$, $-2$, $-3$, and so on. This set, named $\mathbb{Z}$, has the noticeable property that it does not have a lower bound limit (differently from $\mathbb{N}$).
As further extension we can consider to introduce a repeated sum operator, called multiplication, and its inverse, called division. Guess what! While the former operator gives always rise to integer numbers, the latter does not. Indeed, we need to extend further $\mathbb{Z}$ to include new elements. The new set is that of rational numbers, $\mathbb{Q}$, which contains, among the others, the decimal numbers such as $0.1$, $-14.5697$, $3/4$ and so on. Every element of this set can be expressed as a fraction of two integer numbers, and it has two interesting properties: first, you can always find a new rational number that resides between any two rational numbers. Second, oddly enough, the set of rational numbers has the same number of elements than the set of natural numbers!
Now, coming to the last extension, let’s introduce a repeated multiplication operator, called power, and its inverse called root. For example, I can compute the third power of 4, that is $4^3 = 4 \cdot 4 \cdot 4 = 64$. Conversely, I can compute the cubic root of 64 which is $\sqrt[3]{64} = 4$. It goes without saying: the root operator of a rational number does not always exists. There are indeed some numbers which are not rational, that cannot be expressed as a fraction. These numbers, along with the rational ones form the set of real numbers, called $\mathbb{R}$. The number its elements does not coincide any more with that of natural numbers, and its elements are representable with the points of a line. This set has truly a lot of appealing properties that give rise to counterintuitive results!
As a bonus for having read this section, consider the following: while we have extended the rational numbers to be able to compute the root, this was not enough. For example, the square root of a negative, real number is not real. You can proceed and invent your own new numerical set to be able to compute it (and it actually has already been invented). This is left as an exercise!