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Question

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

A
Both (i) and (ii) are uncountably infinite
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B
(i) uncountably infinite and (ii) countably infinite
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C
(i) countably infinite and (ii) uncountably infinite
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D
Both (i) and (ii) are countably infinite
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Solution

The correct option is C (i) countably infinite and (ii) 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.

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