Question

Identify the finite and infinite sets and find the cardinal numbers of the finite sets$.$

$E=\{x:x=\frac{1}{n^2+1},n\in Z\}$

Answer 1

The given set is $E=\{x:x=\frac{1}{n^2+1},n\in Z\}$

In the given set $x=\frac{1}{n^2+1}$and $n\in Z$

put the values of $n$ as $1,2,3,4,........$

Set $E$ can be defined in Roster form as below

$E=\left\{1,\frac{1}{2},\frac{1}{5},\frac{1}{10},\frac{1}{17},.............\right\}$

It is an infinite set$.$

Hence$,$ the given set is an infinite set$.$