7.0 Subsets of the Set $R$

$$\begin{equation} \begin{aligned} i.\,The\;set\;of\;all\;Natural\;numbers\;N = \{ 1,2,3,4,5,6,...\} \\ ii.\;The\;set\;of\;all\;Integers\,\;Z = \{ ...., - 3, - 2, - 1,0,1,2,3,...\} \\ iii.\;The\;set\;of\;all\;Rational\;numbers\;\;Q\; = \{ x:x = {m \over n},\;and\;m,n \in Z,\,\;n \ne 0\} \\ iv.\;The\;set\;fall\;Irrational\;numbers\; = T = \{ x:x \in R\,and\;x \notin Q\} \\\end{aligned} \end{equation} $$

Then,

$$\begin{equation} \begin{aligned} N \subset Z \subset Q \subset R \\ T \subset R\; \\ N\not \subset \;T \\\end{aligned} \end{equation} $$