Question

Which of the following are countably infinite and uncountably infinte.
$\left(i\right)$Set of natural numbers
$\left(ii\right)$Set of real numbers

• A. Both $\left(i\right)$ and $\left(ii\right)$ are uncountably infinite
• B. $\left(i\right)$ uncountably infinite and $\left(ii\right)$ countably infinite
• C. $\left(i\right)$ countably infinite and $\left(ii\right)$ uncountably infinite
• D. Both $\left(i\right)$ and $\left(ii\right)$ are countably infinite

Answer 1

The correct option is C $\left(i\right)$ countably infinite and $\left(ii\right)$ uncountably infinite

Countably Infinite: Set of natural numbers are countably infinite because one can count natural number one after other easily.
Uncountably infinite: Set of real numbers are uncountably infinite because real numbers cannot be counted.