I was recently getting started with mathematic formal notation by defining sets of numbers. In Wikipedia, there are some of them definited as:
$\mathbb{Z} = \{\ldots -3,-2,-1,0,1,2,3\ldots\}$
$\mathbb{Q} = \{ p: \quad p= \frac{a}{b} \quad / \quad a, b \in\mathbb{Z} \quad \land \quad b\neq 0\}$
But I found out, that irrational numbers can't be defined without real numbers, irrational numbers are defined as:
$\mathbb{I}=\mathbb{R}\setminus\mathbb{Q}$
So I was trying to define real numbers but there was no definition for irrational numbers that could help me to define real numbers, so how can I define real numbers in this kind of notation?