This notation is basic number symbol. In south korea, usually learn this number system at high school. Natural number is called "자연수" in korean,
and this only refers positive number. Number is includes natural number, 0, negative number. Therefore, number is bigger concept than natural number.
Rational number and irrational number is contradiction. If one number is rational number, that can't be irrational number. And rational number covers
natural number and number. Finally, real number is biggest concept at here. Actually, we have complex number or other notation, we did not consider at
here. Real number is include a lot of things. Real number covers natural number, number, rational number, irrational number.
Then, why we need to learn this number system? Because, we usually explain social phenomena using real number. For example, GDP growth rate is described number such as 2%, 5%.
Also, when we talk about monetary policy, central bank increased or decreased by 25bp, 50bp, or other base points. Moreover, we usually used rational number not natural number when calculated equilibrium.
How can this calculation? Produced the amount of rational number in real economy is very difficult. But, we used this method. Also, after we learned econometrics, we used probability theory, matrix theory, and others.
However, all of these based on number theory or set theory. Therefore, when we want to good explain or make hypothesis, we using number.
Thus, we will often meet this symbol after learning without direct notation.

Now, we checked many mathematical symbols.

[a,b] := {$$x\in\mathbb{R}$$ := $$a\leq x \leq b$$}: closed interval

(a,b) := {$$x \in \mathbb{R}$$ := a< x< b}: open interval